Mixed Type Partial Differential Equations Lecture Notes On

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Mixed Type Partial Differential Equations, Lecture Notes On

Author : Rassias John Michael
Publisher : World Scientific Publishing Company
ISBN 13 : 9813103647
Total Pages : 152 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Mixed Type Partial Differential Equations, Lecture Notes On by : Rassias John Michael

Download or read book Mixed Type Partial Differential Equations, Lecture Notes On written by Rassias John Michael and published by World Scientific Publishing Company. This book was released on 1990-08-30 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.

Lecture Notes on Mixed Type Partial Differential Equations

Author : John Michael Rassias
Publisher : World Scientific
ISBN 13 : 9789810204068
Total Pages : 160 pages
Book Rating : 4.2/5 (4 download)

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Book Synopsis Lecture Notes on Mixed Type Partial Differential Equations by : John Michael Rassias

Download or read book Lecture Notes on Mixed Type Partial Differential Equations written by John Michael Rassias and published by World Scientific. This book was released on 1990 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book.

Partial Differential Equations

Author : Walter A. Strauss
Publisher : John Wiley & Sons
ISBN 13 : 0470054565
Total Pages : 467 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Partial Differential Equations by : Walter A. Strauss

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Elliptic–Hyperbolic Partial Differential Equations

Author : Thomas H. Otway
Publisher : Springer
ISBN 13 : 3319197614
Total Pages : 134 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Elliptic–Hyperbolic Partial Differential Equations by : Thomas H. Otway

Download or read book Elliptic–Hyperbolic Partial Differential Equations written by Thomas H. Otway and published by Springer. This book was released on 2015-07-08 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy

Author : Guo Chun Wen
Publisher : World Scientific
ISBN 13 : 9812779434
Total Pages : 453 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by : Guo Chun Wen

Download or read book Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy written by Guo Chun Wen and published by World Scientific. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias. The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above TricomiOCo Bers and TricomiOCoFranklOCoRassias problems can be solved. Sample Chapter(s). Chapter 1: Elliptic Complex Equations of First Order (247 KB). Contents: Elliptic Complex Equations of First Order; Elliptic Complex Equations of Second Order; Hyperbolic Complex Equations of First and Second Orders; First Order Complex Equations of Mixed Type; Second Order Linear Equations of Mixed Type; Second Order Quasilinear Equations of Mixed Type. Readership: Graduate students and academics in analysis, differential equations and applied mathematics.

Introduction to Partial Differential Equations

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 3319020994
Total Pages : 636 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Introduction to Partial Differential Equations by : Peter J. Olver

Download or read book Introduction to Partial Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Boundary Value Problems, Integral Equations and Related Problems

Author : Guo Chun Wen
Publisher : World Scientific
ISBN 13 : 9814327867
Total Pages : 436 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Boundary Value Problems, Integral Equations and Related Problems by : Guo Chun Wen

Download or read book Boundary Value Problems, Integral Equations and Related Problems written by Guo Chun Wen and published by World Scientific. This book was released on 2011 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, and others.

Control Systems and Mathematical Methods in Economics

Author : Gustav Feichtinger
Publisher : Springer
ISBN 13 : 3319751697
Total Pages : 443 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Control Systems and Mathematical Methods in Economics by : Gustav Feichtinger

Download or read book Control Systems and Mathematical Methods in Economics written by Gustav Feichtinger and published by Springer. This book was released on 2018-06-08 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

Lectures on Partial Differential Equations

Author : G. B. Folland
Publisher : Springer
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Lectures on Partial Differential Equations by : G. B. Folland

Download or read book Lectures on Partial Differential Equations written by G. B. Folland and published by Springer. This book was released on 1983 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress

Author : Michael Ruzhansky
Publisher : World Scientific
ISBN 13 : 9814464708
Total Pages : 668 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress by : Michael Ruzhansky

Download or read book Progress In Analysis And Its Applications - Proceedings Of The 7th International Isaac Congress written by Michael Ruzhansky and published by World Scientific. This book was released on 2010-07-29 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Society for Analysis, its Applications and Computation (ISAAC) has held its international congresses biennially since 1997. This proceedings volume reports on the progress in analysis, applications and computation in recent years as covered and discussed at the 7th ISAAC Congress. This volume includes papers on partial differential equations, function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 500 participants from almost 60 countries attending the congress, the book comprises a broad selection of contributions in different topics.

Partial Differential Equations and Boundary-Value Problems with Applications

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821868896
Total Pages : 545 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Partial Differential Equations and Boundary-Value Problems with Applications by : Mark A. Pinsky

Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Counter Examples In Differential Equations And Related Topics: A Collection Of Counter Examples

Author : John Michael Rassias
Publisher : World Scientific Publishing Company
ISBN 13 : 9813103590
Total Pages : 194 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Counter Examples In Differential Equations And Related Topics: A Collection Of Counter Examples by : John Michael Rassias

Download or read book Counter Examples In Differential Equations And Related Topics: A Collection Of Counter Examples written by John Michael Rassias and published by World Scientific Publishing Company. This book was released on 1991-04-22 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of counter-examples highlights the theory of differential equations and related topics which is now playing an enormously important role in the area of science, engineering and mathematics.

Introduction to Partial Differential Equations

Author : Aslak Tveito
Publisher : Springer Science & Business Media
ISBN 13 : 0387227733
Total Pages : 402 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Introduction to Partial Differential Equations by : Aslak Tveito

Download or read book Introduction to Partial Differential Equations written by Aslak Tveito and published by Springer Science & Business Media. This book was released on 2008-01-21 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

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)

Discontinuous Galerkin Methods

Author : Bernardo Cockburn
Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn

Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Finite Difference Methods for Ordinary and Partial Differential Equations

Author : Randall J. LeVeque
Publisher : SIAM
ISBN 13 : 9780898717839
Total Pages : 356 pages
Book Rating : 4.7/5 (178 download)

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Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque

Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Treatise on Analysis

Author : J. Dieudonné
Publisher : Academic Press
ISBN 13 : 1483144968
Total Pages : 387 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Treatise on Analysis by : J. Dieudonné

Download or read book Treatise on Analysis written by J. Dieudonné and published by Academic Press. This book was released on 2014-07-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treatise on Analysis, Volume 10–VII provides information pertinent to the fundamental aspects of linear functional equations. This book discusses the problems dealing with functional equations of scalar or of vectors. Comprised of one chapter, this volume begins with a description and study of the primary concepts and tools that have prompted the progress in the study of linear partial differential equations. This text then explains the importance of the integral operators. The reader is also introduced to integral operators that operate not only on vector function, but also on sections of vector bundles. This book discusses as well the applications of the differential operators to spectral theory. This book is a valuable resource for mathematicians.