The extensive application of modern mathematical teehniques to theoretical and mathematical physics requires a fresh approach to the course of equations of mathematical physics. This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem. The concept of a generalized solution considerably broadens the field of problems and enables solving from a unified position the most interesting problems that cannot be solved by applying elassical methods. To this end two new courses have been written at the Department of Higher Mathematics at the Moscow Physics anrl Technology Institute, namely, "Equations of Mathematical Physics" by V. S. Vladimirov and "Partial Differential Equations" by V. P. Mikhailov (both books have been translated into English by Mir Publishers, the first in 1984 and the second in 1978). The present collection of problems is based on these courses and amplifies them considerably. Besides the classical boundary value problems, we have ineluded a large number of boundary value problems that have only generalized solutions. Solution of these requires using the methods and results of various branches of modern analysis. For this reason we have ineluded problems in Lebesgue in tegration, problems involving function spaces (especially spaces of generalized differentiable functions) and generalized functions (with Fourier and Laplace transforms), and integral equations.

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Bibliographic Information

Book Title: A Collection of Problems on the Equations of Mathematical Physics
Editors: V. S. Vladimirov
DOI: https://doi.org/10.1007/978-3-662-05558-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1986
Softcover ISBN: 978-3-662-05560-1Published: 16 April 2014
eBook ISBN: 978-3-662-05558-8Published: 09 November 2013
Edition Number: 1
Number of Pages: 288
Number of Illustrations: 1 b/w illustrations
Additional Information: Jointly published with MIR Publishers, Moscow. Title of the Russian original edition: Glavnaja redakcija fiziko-matematiceskoj literatury
Topics: Theoretical, Mathematical and Computational Physics

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Table of contents (6 papers)

Front Matter

Symbols and Definitions

Statement of Boundary Value Problems in Mathematical Physics

Function Spaces and Integral Equations

Generalized Functions

The Cauchy Problem

Boundary Value Problems for Equations of Elliptic Type

Back Matter

About this book