Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations (Encyclopaedia of Mathematical Sciences)

Egorov, IU. V.

ISBN 10: 0387520031 / ISBN 13: 9780387520032

Published by Springer Verlag, 1991

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Bibliographic Details

• Title: Partial Differential Equations III: The Cauchy Problem. Qualitative Theory of Partial Differential Equations (Encyclopaedia of Mathematical Sciences)
• Publisher: Springer Verlag
• Publication Date: 1991
• Language: English
• ISBN 10: 0387520031
• ISBN 13: 9780387520032
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

Two general questions regarding partial differential equations are explored in detail in this volume of the Encyclopaedia. The first is the Cauchy problem, and its attendant question of well-posedness (or correctness). The authors address this question in the context of PDEs with constant coefficients and more general convolution equations in the first two chapters. The third chapter extends a number of these results to equations with variable coefficients. The second topic is the qualitative theory of second order linear PDEs, in particular, elliptic and parabolic equations. Thus, the second part of the book is primarily a look at the behavior of solutions of these equations. There are versions of the maximum principle, the Phragmen-Lindelöf theorem and Harnack's inequality discussed for both elliptic and parabolic equations. The book is intended for readers who are already familiar with the basic material in the theory of partial differential equations.