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On The Uniqueness Of Generalized Solutions Of First Order Quasilinear Partial Differential Equations
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Book Synopsis On the Uniqueness of Generalized Solutions of First Order, Quasilinear Partial Differential Equations by : Avron Douglis
Download or read book On the Uniqueness of Generalized Solutions of First Order, Quasilinear Partial Differential Equations written by Avron Douglis and published by . This book was released on 1960 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Uniqueness of Generalized Solutions of First Order, Quasilinear Partial Differential Equations by : Avron Douglis
Download or read book On the Uniqueness of Generalized Solutions of First Order, Quasilinear Partial Differential Equations written by Avron Douglis and published by . This book was released on 1960 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and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.
Book Synopsis Partial Differential Equations by : Phoolan Prasad
Download or read book Partial Differential Equations written by Phoolan Prasad and published by New Age International. This book was released on 1985 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.
Book Synopsis Partial Differential Equations by : Bode Vladimov
Download or read book Partial Differential Equations written by Bode Vladimov and published by Createspace Independent Publishing Platform. This book was released on 2016-12-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of partial differential equations is written for the reader who likes rigorous and unhurried mathematical texts, and understands that reading such texts actually saves the time and effort. The main topics of the book cover the standard topics in an undergraduate course in PDE: we give a detailed account on change of variables in PDEs; consider first-order linear and semilinear equations (obtaining general solutions with the use of method of characteristics); study characteristic systems associated with first-order quasilinear equation and their first integrals; description of solution sets of first-order quasilinear equations; method of characteristics for first-order quasilinear equations, and second-order semilinear equations. The books is essentially, save a number of references to the multi-variable calculus and ordinary differential equations, self-contained. Throughout the book we give numerous, detailed, and workable examples on the use of Maple and the popular online resource Wolfram Alpha for dealing with problems in the theory of partial differential equations.
Book Synopsis Generalized Solutions of Functional Differential Equations by : Joseph Wiener
Download or read book Generalized Solutions of Functional Differential Equations written by Joseph Wiener and published by World Scientific. This book was released on 1993 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need to investigate functional differential equations with discontinuous delays is addressed in this book. Recording the work and findings of several scientists on differential equations with piecewise continuous arguments over the last few years, this book serves as a useful source of reference. Great interest is placed on discussing the stability, oscillation and periodic properties of the solutions. Considerable attention is also given to the study of initial and boundary-value problems for partial differential equations of mathematical physics with discontinuous time delays. In fact, a large part of the book is devoted to the exploration of differential and functional differential equations in spaces of generalized functions (distributions) and contains a wealth of new information in this area. Each topic discussed appears to provide ample opportunity for extending the known results. A list of new research topics and open problems is also included as an update.
Book Synopsis Partial Differential Equations by : F. John
Download or read book Partial Differential Equations written by F. John and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. Added to this second corrected edition is a collection of problems and solutions, which illustrate and supplement the theories developed in the text. Fritz John New York September, 1974 vii TABLE OF CONTENTS Introd uction 1 CHAPrER I - THE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 2. The general first order equation for a function of two variables. • • • • • • • • • 15 The general first order equation for a function 3. of n independent variables. • • • • • 37 CHAPrER II - THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS 1. Analytic functions of several real variables • 48 2. Formulation of the Cauchy problem. The notion of characteristics. • • • 54 3. The Cauchy problem for the general non-linear equation ••• 71 4. The Cauchy-Kowalewsky theorem. 76 CHAPTER III - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.
Book Synopsis Generalized Solutions to Functional Partial Differential Equations of the First Order by : Jan Turo
Download or read book Generalized Solutions to Functional Partial Differential Equations of the First Order written by Jan Turo and published by . This book was released on 1988 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations by : Marcelo Epstein
Download or read book Partial Differential Equations written by Marcelo Epstein and published by Springer. This book was released on 2017-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.
Book Synopsis Beginning Partial Differential Equations by : Peter V. O'Neil
Download or read book Beginning Partial Differential Equations written by Peter V. O'Neil and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, yet accessible, introduction to partial differential equations—updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addressing more specialized topics and applications. Maintaining the hallmarks of the previous edition, the book begins with first-order linear and quasi-linear PDEs and the role of characteristics in the existence and uniqueness of solutions. Canonical forms are discussed for the linear second-order equation, along with the Cauchy problem, existence and uniqueness of solutions, and characteristics as carriers of discontinuities in solutions. Fourier series, integrals, and transforms are followed by their rigorous application to wave and diffusion equations as well as to Dirichlet and Neumann problems. In addition, solutions are viewed through physical interpretations of PDEs. The book concludes with a transition to more advanced topics, including the proof of an existence theorem for the Dirichlet problem and an introduction to distributions. Additional features of the Second Edition include solutions by both general eigenfunction expansions and numerical methods. Explicit solutions of Burger's equation, the telegraph equation (with an asymptotic analysis of the solution), and Poisson's equation are provided. A historical sketch of the field of PDEs and an extensive section with solutions to selected problems are also included. Beginning Partial Differential Equations, Second Edition is an excellent book for advanced undergraduate- and beginning graduate-level courses in mathematics, science, and engineering.
Book Synopsis Partial Differential Equations by : Fritz John
Download or read book Partial Differential Equations written by Fritz John and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. In the present edition, only minor corrections have been made in the text. An Index and up-to-date listing of books recommended for further study have been added. Fritz John New York November 19, 1970 v TABLE OF CONTENTS Introduetion 1 CHAPl'ER I - TEE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 The general first order equation for a funetion 2. of two variables. • • • • • • • • • 15 The general first order equation for a funetion 3. of n independent variables. • • • • • 37 CHAPl'ER II - TEE CAUCIIT PROBLEM FOR HIGEER ORDER EQUATIONS 1. Analytie funetions of several real variables • Formulation of the Cauehy problem. The not ion 2. of eharaeteristies. • • • 54 3. The Cauehy problem for the general non-linear equation. 71 4. The Cauehy-Kowalewsky theorem. 76 CHAPl'ER 111 - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.
Book Synopsis On Calculating Solutions of Quasi-linear, First Order Partial Differential Equations by : AVRON. DOUGLIS
Download or read book On Calculating Solutions of Quasi-linear, First Order Partial Differential Equations written by AVRON. DOUGLIS and published by . This book was released on 1960 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics by : Victor A. Galaktionov
Download or read book Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics written by Victor A. Galaktionov and published by CRC Press. This book was released on 2006-11-02 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Book Synopsis Introduction to Partial Differential Equations and Boundary Value Problems by : Rene Dennemeyer
Download or read book Introduction to Partial Differential Equations and Boundary Value Problems written by Rene Dennemeyer and published by . This book was released on 1968 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis First-Order Partial Differential Equations, Vol. 1 by : Hyun-Ku Rhee
Download or read book First-Order Partial Differential Equations, Vol. 1 written by Hyun-Ku Rhee and published by Courier Corporation. This book was released on 2014-05-05 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of most sections. This volume is geared to advanced undergraduates or first-year grad students with a sound understanding of calculus and elementary ordinary differential equations. 1986 edition. 189 black-and-white illustrations. Author and subject indices.
Book Synopsis On Discontinuous Solutions of Quasi-linear First Order Partial Differential Equations by : AVRON. DOUGLIS
Download or read book On Discontinuous Solutions of Quasi-linear First Order Partial Differential Equations written by AVRON. DOUGLIS and published by . This book was released on 1960 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear and Nonlinear Waves by : G. B. Whitham
Download or read book Linear and Nonlinear Waves written by G. B. Whitham and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
