Initial Boundary Value Problems in Mathematical Physics PDF Download
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Author: Rolf Leis
Publisher: Courier Corporation
ISBN: 0486315827
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Introduction to classical scattering theory and time-dependent theory of linear equations in mathematical physics. Topics include wave operators, exterior boundary value problems, radiation conditions, limiting absorption principles, and more. 1986 edition.
Author: Rolf Leis
Publisher: Courier Corporation
ISBN: 0486315827
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Introduction to classical scattering theory and time-dependent theory of linear equations in mathematical physics. Topics include wave operators, exterior boundary value problems, radiation conditions, limiting absorption principles, and more. 1986 edition.
Author: O.A. Ladyzhenskaya
Publisher: Springer Science & Business Media
ISBN: 1475743173
Category : Science
Languages : en
Pages : 350
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Book Description
In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.
Author: Rolf Leis
Publisher:
ISBN: 9780598049049
Category :
Languages : en
Pages : 274
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Book Description
Author: Olʹga A. Ladyženskaja
Publisher: American Mathematical Soc.
ISBN: 9780821830109
Category : Boundary value problems
Languages : en
Pages : 218
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Book Description
Author: Athanassios S. Fokas
Publisher: SIAM
ISBN: 089871706X
Category : Mathematics
Languages : en
Pages : 328
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Book Description
This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Author: Athanasios S. Fokas
Publisher: SIAM
ISBN: 1611973813
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Author: Stefan Bergman
Publisher: Courier Corporation
ISBN: 0486445534
Category : Mathematics
Languages : en
Pages : 450
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Book Description
This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
Author: Rolf Leis
Publisher: Springer-Verlag
ISBN: 3663106497
Category : Technology & Engineering
Languages : de
Pages : 273
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Book Description
Author: Mark A. Pinsky
Publisher: American Mathematical Soc.
ISBN: 0821868896
Category : Mathematics
Languages : en
Pages : 545
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Book Description
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.
Author: A. A. Samarskii
Publisher: Walter de Gruyter
ISBN: 3110205793
Category : Mathematics
Languages : en
Pages : 453
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Book Description
The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.
