The Characteristic Method And Its Generalizations For First Order Nonlinear Partial Differential Equations

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The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations

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Author : Tran Duc Van
Publisher : CRC Press
ISBN 13 : 9781584880165
Total Pages : 256 pages
Book Rating : 4.8/5 (81 download)

Book Synopsis The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations by : Tran Duc Van

Download or read book The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations written by Tran Duc Van and published by CRC Press. This book was released on 1999-06-25 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.

Characteristic Method and Its Generalizations for First-Order Nonlinear Pde

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Author : Duc Van Tran
Publisher :
ISBN 13 : 9780582414303
Total Pages : pages
Book Rating : 4.4/5 (143 download)

Book Synopsis Characteristic Method and Its Generalizations for First-Order Nonlinear Pde by : Duc Van Tran

Download or read book Characteristic Method and Its Generalizations for First-Order Nonlinear Pde written by Duc Van Tran and published by . This book was released on 1999-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Characteristic Method and Its Generalizations for First-Order Nonl inear Partial Differential Equations represents a comprehensive exposi tion of the authors' works over the last decade. The book is self-cont ained and assumes only basic measure theory, topology, and ordinary di fferential equations as prerequisites. With its innovative approach, n ew results, and many applications, it will prove valuable to mathemati cians, physicists, and engineers and especially interesting to researc hers in nonlinear PDEs, differential inequalities, multivalued analysi s, differential games, and related topics in applied analysis.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

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Author : Inna Shingareva
Publisher : Springer Science & Business Media
ISBN 13 : 370910517X
Total Pages : 357 pages
Book Rating : 4.7/5 (91 download)

Book Synopsis Solving Nonlinear Partial Differential Equations with Maple and Mathematica by : Inna Shingareva

Download or read book Solving Nonlinear Partial Differential Equations with Maple and Mathematica written by Inna Shingareva and published by Springer Science & Business Media. This book was released on 2011-07-24 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

Nonlinear Partial Differential Equations for Scientists and Engineers

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Author : Lokenath Debnath
Publisher : Springer Science & Business Media
ISBN 13 : 0817644180
Total Pages : 738 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Nonlinear Partial Differential Equations for Scientists and Engineers by : Lokenath Debnath

Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2010-02-20 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.

Using the Mathematics Literature

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Author : Kristine K. Fowler
Publisher : CRC Press
ISBN 13 : 9780824750350
Total Pages : 412 pages
Book Rating : 4.7/5 (53 download)

Book Synopsis Using the Mathematics Literature by : Kristine K. Fowler

Download or read book Using the Mathematics Literature written by Kristine K. Fowler and published by CRC Press. This book was released on 2004-05-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Handbook of Mathematics for Engineers and Scientists

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Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1420010514
Total Pages : 1542 pages
Book Rating : 4.4/5 (2 download)

Book Synopsis Handbook of Mathematics for Engineers and Scientists by : Andrei D. Polyanin

Download or read book Handbook of Mathematics for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2006-11-27 with total page 1542 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgr

Thermo-Mechanics Applications and Engineering Technology

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Author : Zied Driss
Publisher : Springer
ISBN 13 : 3319709577
Total Pages : 241 pages
Book Rating : 4.3/5 (197 download)

Book Synopsis Thermo-Mechanics Applications and Engineering Technology by : Zied Driss

Download or read book Thermo-Mechanics Applications and Engineering Technology written by Zied Driss and published by Springer. This book was released on 2018-01-30 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the dissemination of information of permanent interest in thermo-mechanics applications and engineering technology. Contributions have clear relevance to industrial device and a relatively straightforward or feasible path to application. Chapters are sought that have long-term relevance to specific applications including convective heat transfer, fluid mechanics, combustion, aerodynamics, hydrodynamics, turbomachinery and multi-phase flows. In fact, many aspects in industrial operations and daily life are closely related to thermo-mechanics processes. Along with the development of computer industry and the advancement of numerical methods, solid foundation in both hardware and software has been established to study the processes by using numerical simulation methods, which play important roles in the ways of extending research topics, reducing research costs, discovering new phenomena, and developing new technologies. The presented case studies and development approaches aim to provide the readers, such as engineers and PhD students, with basic and applied studies broadly related to the Thermo-Mechanics Applications and Engineering Technology.

Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations

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Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9812794557
Total Pages : 473 pages
Book Rating : 4.8/5 (127 download)

Book Synopsis Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations by : Helmut Florian

Download or read book Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations written by Helmut Florian and published by World Scientific. This book was released on 2001 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.

Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop

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Author : Helmut Florian
Publisher : World Scientific
ISBN 13 : 9814490008
Total Pages : 473 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop by : Helmut Florian

Download or read book Functional-analytic And Complex Methods, Their Interactions, And Applications To Partial Differential Equations - Proceedings Of The International Graz Workshop written by Helmut Florian and published by World Scientific. This book was released on 2001-11-12 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws. remove /a remove

Abstract and Applied Analysis

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Author : N. M. Chuong
Publisher : World Scientific
ISBN 13 : 9812702547
Total Pages : 579 pages
Book Rating : 4.8/5 (127 download)

Book Synopsis Abstract and Applied Analysis by : N. M. Chuong

Download or read book Abstract and Applied Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2004 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material OCo the coefficients may jump from domain to domain; Stochastic Analysis OCo many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Deterministic Analysis: Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes); On the Lagrange Problem About the Strongest Columns (Yu V Egorov); Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider); Semi-Classical Methods in GinzburgOCoLandau Theory (B Helffer); Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto); Estimates for Elliptic Systems for Composite Material (L Nirenberg); On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm); Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto); Stochastic Analysis: Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed); Some of Future Directions of White Noise Analysis (T Hida); Constructing Random Probability Distributions (T P Hill & D E R Sitton); Multiparameter Additive Processes of Mixture Type (K Inoue); The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek); Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato); and other papers. Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics."

Abstract and Applied Analysis

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Author : N M Chuong
Publisher : World Scientific
ISBN 13 : 9814482110
Total Pages : 580 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Abstract and Applied Analysis by : N M Chuong

Download or read book Abstract and Applied Analysis written by N M Chuong and published by World Scientific. This book was released on 2004-06-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods. Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Deterministic Analysis:Differentiation of Hypergeometric Functions with Respect to Parameters (Yu A Brychkov & K O Geddes)On the Lagrange Problem About the Strongest Columns (Yu V Egorov)Wavelet Based Fast Solution of Boundary Integral Equations (H Harbrecht & R Schneider)Semi-Classical Methods in Ginzburg–Landau Theory (B Helffer)Stability of Equilibriums in One-Dimensional Motion of Compressible Viscous Gas Forced by Self-Gravity (Y Iwata & Y Yamamoto)Estimates for Elliptic Systems for Composite Material (L Nirenberg)On Asymptotics for the Mabuchi Energy Functional (D H Phong & J Sturm)Regularity of Solutions of the Initial Boundary Value Problem for Linearized Equations of Ideal Magneto-Hydrodynamics (M Yamamoto)Stochastic Analysis:Impulsive Stochastic Evolution Inclusions with Multi-Valued Diffusion (N U Ahmed)Some of Future Directions of White Noise Analysis (T Hida)Constructing Random Probability Distributions (T P Hill & D E R Sitton)Multiparameter Additive Processes of Mixture Type (K Inoue)The Random Integral Representation Hypothesis Revisited: New Classes of S-Selfdecomposable Laws (Z J Jurek)Semigroups and Processes with Parameter in a Cone (J Pedersen & K-I Sato)and other papers Readership: Researchers and academics in the fields of analysis and differential equations, approximation theory, probability and statistics. Keywords:Almost Complex Manifolds;Noncommutative Geometry;Lagrange Problem;Boundary Value Problem

Nonlinear Partial Differential Equations

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Author : W. F. Ames
Publisher : Academic Press
ISBN 13 : 1483221504
Total Pages : 332 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Nonlinear Partial Differential Equations by : W. F. Ames

Download or read book Nonlinear Partial Differential Equations written by W. F. Ames and published by Academic Press. This book was released on 2014-05-12 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.

Nonlinear Waves: A Geometrical Approach

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Author : Angela Slavova
Publisher : World Scientific Publishing
ISBN 13 : 9813271620
Total Pages : 208 pages
Book Rating : 4.8/5 (132 download)

Book Synopsis Nonlinear Waves: A Geometrical Approach by : Angela Slavova

Download or read book Nonlinear Waves: A Geometrical Approach written by Angela Slavova and published by World Scientific Publishing. This book was released on 2018-11-16 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Advances in Deterministic and Stochastic Analysis

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Author : N. M. Chuong
Publisher : World Scientific
ISBN 13 : 9812770496
Total Pages : 372 pages
Book Rating : 4.8/5 (127 download)

Book Synopsis Advances in Deterministic and Stochastic Analysis by : N. M. Chuong

Download or read book Advances in Deterministic and Stochastic Analysis written by N. M. Chuong and published by World Scientific. This book was released on 2007 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects articles in pure and applied analysis, partial differential equations, geometric analysis and stochastic and infinite-dimensional analysis. In particular, the contributors discuss integral and pseudo-differential operators, which play an important role in partial differential equations. Other methods of solving the partial differential equations are considered, such as the min-max approach to variational problems and boundary value problems. The foundations of quantum mechanics from the viewpoints of infinite-dimensional spaces and Bell''s inequality and contraction are also mentioned.

Calculus Without Derivatives

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Author : Jean-Paul Penot
Publisher : Springer Science & Business Media
ISBN 13 : 1461445388
Total Pages : 541 pages
Book Rating : 4.4/5 (614 download)

Book Synopsis Calculus Without Derivatives by : Jean-Paul Penot

Download or read book Calculus Without Derivatives written by Jean-Paul Penot and published by Springer Science & Business Media. This book was released on 2012-11-09 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

Annales Polonici Mathematici

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Author :
Publisher :
ISBN 13 :
Total Pages : 318 pages
Book Rating : 4.3/5 (91 download)

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Download or read book Annales Polonici Mathematici written by and published by . This book was released on 2003 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Atti del Seminario matematico e fisico dell'Università di Modena e Reggio Emilia

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Author :
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Atti del Seminario matematico e fisico dell'Università di Modena e Reggio Emilia by :

Download or read book Atti del Seminario matematico e fisico dell'Università di Modena e Reggio Emilia written by and published by . This book was released on 2005 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: