Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions

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Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions, Functional Problems And Applications

Author : Minhos Feliz Manuel
Publisher : World Scientific
ISBN 13 : 9813220074
Total Pages : 216 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions, Functional Problems And Applications by : Minhos Feliz Manuel

Download or read book Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions, Functional Problems And Applications written by Minhos Feliz Manuel and published by World Scientific. This book was released on 2017-08-23 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm–Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators. The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line. Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases. The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved. Contents: Boundary Value Problems on the Half-Line: Third-Order Boundary Value ProblemsGeneral nth-Order ProblemsImpulsive Problems on the Half-Line with Infinite Impulse MomentsHomoclinic Solutions and Lidstone Problems: Homoclinic Solutions for Second-Order ProblemsHomoclinic Solutions to Fourth-Order ProblemsLidstone Boundary Value ProblemsHeteroclinic Solutions and Hammerstein Equations: Heteroclinic Solutions for Semi-Linear Problems (i)Heteroclinic Solutions for Semi-Linear Problems (ii)Heteroclinic Solutions for Semi-Linear Problems (iii)Hammerstein Integral Equations with Sign-Changing KernelsFunctional Boundary Value Problems: Second-Order Functional ProblemsThird-Order Functional Problemsϕ-Laplacian Equations with Functional Boundary Conditions Readership: Graduate students and researchers interested in nonlinear analysis. Keywords: Boundary Value Problems in Unbounded Domains;Impulsive Problems with Infinite Impulses;Homoclinic Solutions;Lidstone Problems on the Real Line;Heteroclinic Solutions for Hammerstein Equations;Functional ProblemsReview: Key Features: Presents higher order boundary value and impulsive problems on unbounded domainsElucidates homoclinic and heteroclinic solutions without growth, sign or periodicity assumptions on the nonlinearity, and their relation with Lidstone problems and Hammerstein equations on the real lineExplains clearly the semi-linear and higher order functional problems where the boundary conditions can include nonlocal data and global variation on the unknown functions, such as multi-point, integral, maximum and/or minimum arguments

Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions

Author : Feliz Manuel Minhós
Publisher :
ISBN 13 : 9789813220065
Total Pages : 217 pages
Book Rating : 4.2/5 (2 download)

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Book Synopsis Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions by : Feliz Manuel Minhós

Download or read book Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions written by Feliz Manuel Minhós and published by . This book was released on 2017 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm–Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators. The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line. Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases. The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved."--Publisher's website.

Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains

Download Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains PDF Online Free

Author : Feliz Manuel Minhos
Publisher : World Scientific
ISBN 13 : 9811225141
Total Pages : 243 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains by : Feliz Manuel Minhos

Download or read book Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains written by Feliz Manuel Minhos and published by World Scientific. This book was released on 2022-04-11 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.

Ordinary Differential Equations and Boundary Value Problems

Author : John R Graef
Publisher : World Scientific
ISBN 13 : 9813236477
Total Pages : 176 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Ordinary Differential Equations and Boundary Value Problems by : John R Graef

Download or read book Ordinary Differential Equations and Boundary Value Problems written by John R Graef and published by World Scientific. This book was released on 2018-02-13 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book. The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well. Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems. Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs. Contents: Systems of Differential EquationsContinuation of Solutions and Maximal Intervals of ExistenceSmooth Dependence on Initial Conditions and Smooth Dependence on a ParameterSome Comparison Theorems and Differential InequalitiesLinear Systems of Differential EquationsPeriodic Linear Systems and Floquet TheoryStability TheoryPerturbed Systems and More on Existence of Periodic Solutions Readership: Graduate students and researchers interested in ordinary differential equations. Keywords: Differential Equations;Linear Systems;Comparison Theorems;Differential Inequalities;Periodic Systems;Floquet Theory;Stability Theory;Perturbed Equations;Periodic SolutionsReview: Key Features: Clarity of presentationTreatment of linear and nonlinear problemsIntroduction to stability theoryNonroutine exercises to expand insight into more difficult conceptsExamples provided with thorough explanations

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems

Author : Graef John R
Publisher : World Scientific
ISBN 13 : 9813274042
Total Pages : 344 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems by : Graef John R

Download or read book Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems written by Graef John R and published by World Scientific. This book was released on 2018-09-18 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.

Boundary Value Problems For Fractional Differential Equations And Systems

Author : Bashir Ahmad
Publisher : World Scientific
ISBN 13 : 9811224471
Total Pages : 468 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Boundary Value Problems For Fractional Differential Equations And Systems by : Bashir Ahmad

Download or read book Boundary Value Problems For Fractional Differential Equations And Systems written by Bashir Ahmad and published by World Scientific. This book was released on 2021-02-18 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.

Coincidence Degree and Nonlinear Differential Equations

Author : R. E. Gaines
Publisher : Springer
ISBN 13 : 3540375015
Total Pages : 267 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Coincidence Degree and Nonlinear Differential Equations by : R. E. Gaines

Download or read book Coincidence Degree and Nonlinear Differential Equations written by R. E. Gaines and published by Springer. This book was released on 2006-11-15 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Strong Nonlinear Limit-point/limit-circle Problem

Author : Graef John R
Publisher : World Scientific
ISBN 13 : 9813226390
Total Pages : 324 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Strong Nonlinear Limit-point/limit-circle Problem by : Graef John R

Download or read book The Strong Nonlinear Limit-point/limit-circle Problem written by Graef John R and published by World Scientific. This book was released on 2017-10-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated. Contents: The Origins of the Limit-Point/Limit-Circle ProblemEquations with p-LaplacianStrong Limit-Point/Limit-Circle PropertiesDamped EquationsHigher Order EquationsDelay Equations IDelay Equations IITransformations of the Basic EquationNotes, Open Problems, and Future Directions Readership: Graduate students and researchers of mathematics integrated in limit-point/limit circle topics. Keywords: Limit-Point Problem;Limit-Circle Problem;Strong Limit-Point Problem;Strong Limit-Circle Problem;Asymptotic Properties of Solutions;Nonlinear Differential Equations;Second Order Equations;Higher Order EquationsReview: Key Features: There is no other source of results on this problem except for the individual papers that appear in the literature. This work collects all that is known about this problem in one placeThe references on the nonlinear problem are complete up to 2017Directions for future research are indicated

Partial Differential Equations of Elliptic Type

Author : C. Miranda
Publisher : Springer Science & Business Media
ISBN 13 : 3642877737
Total Pages : 384 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Partial Differential Equations of Elliptic Type by : C. Miranda

Download or read book Partial Differential Equations of Elliptic Type written by C. Miranda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.

Theoretical and Mathematical Physics

Author : Vasiliĭ Sergeevich Vladimirov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831199
Total Pages : 270 pages
Book Rating : 4.8/5 (311 download)

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Book Synopsis Theoretical and Mathematical Physics by : Vasiliĭ Sergeevich Vladimirov

Download or read book Theoretical and Mathematical Physics written by Vasiliĭ Sergeevich Vladimirov and published by American Mathematical Soc.. This book was released on 1988 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Developments in the Solution of Nonlinear Differential Equations

Author : Bruno Carpentieri
Publisher : BoD – Books on Demand
ISBN 13 : 1839686561
Total Pages : 374 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Recent Developments in the Solution of Nonlinear Differential Equations by : Bruno Carpentieri

Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-09-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Boundary Value Problems From Higher Order Differential Equations

Author : Ravi P Agarwal
Publisher : World Scientific
ISBN 13 : 9814513636
Total Pages : 321 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Boundary Value Problems From Higher Order Differential Equations by : Ravi P Agarwal

Download or read book Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1986-07-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems

Elliptic Partial Differential Equations

Author : Vitaly Volpert
Publisher : Springer Science & Business Media
ISBN 13 : 3034605374
Total Pages : 649 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Elliptic Partial Differential Equations by : Vitaly Volpert

Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert and published by Springer Science & Business Media. This book was released on 2011-03-03 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

Proceedings of the St. Petersburg Mathematical Society

Author : Nina Nikolaevna Uralceva (Mathematikerin.)
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890752
Total Pages : 248 pages
Book Rating : 4.8/5 (97 download)

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Book Synopsis Proceedings of the St. Petersburg Mathematical Society by : Nina Nikolaevna Uralceva (Mathematikerin.)

Download or read book Proceedings of the St. Petersburg Mathematical Society written by Nina Nikolaevna Uralceva (Mathematikerin.) and published by American Mathematical Soc.. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Differential Equations: Evolutionary Equations

Author : C.M. Dafermos
Publisher : Elsevier
ISBN 13 : 0080931979
Total Pages : 609 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Differential Equations: Evolutionary Equations by : C.M. Dafermos

Download or read book Handbook of Differential Equations: Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2008-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Author : Hamid Bellout
Publisher : Springer Science & Business Media
ISBN 13 : 3319008919
Total Pages : 583 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow by : Hamid Bellout

Download or read book Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow written by Hamid Bellout and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.

The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type

Author : Thomas H. Otway
Publisher : Springer Science & Business Media
ISBN 13 : 3642244149
Total Pages : 219 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type by : Thomas H. Otway

Download or read book The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type written by Thomas H. Otway and published by Springer Science & Business Media. This book was released on 2012-01-07 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)