Nonlinear partial differential equations of second order

Bibliographic Information

Nonlinear partial differential equations of second order

Guangchang Dong

(Translations of mathematical monographs, v. 95)

American Mathematical Society, c1991

Other Title

非線性二階偏微分方程

Fei hsien hsing erh chieh pʿien wei fen fang chʿeng

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Note

Translated from the Chinese by Kai Seng Chou [Kaising Tso]

Includes bibliographical references (p. 247-249)

Description and Table of Contents

Description

This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

Table of Contents

The first boundary value problem for second-order quasilinear parabolic equations with principal part in divergence form A periodic boundary value problem for a nonlinear telegraph equation The initial value problem for a nonlinear Schrodinger equation Multi-dimensional subsonic flows around an obstacle The initial-boundary value problem for degenerate quasilinear parabolic equations The speed of propagation of the solution of a degenerate quasilinear parabolic equation Aleksandrov and Bony maximum principles for parabolic equations The density theorem and its applications Fully nonlinear parabolic equations Fully nonlinear parabolic equations (continued).

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