Nonlinear partial differential equations of second order
著者
書誌事項
Nonlinear partial differential equations of second order
（Translations of mathematical monographs, v. 95）
American Mathematical Society, c1991
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非線性二階偏微分方程
Fei hsien hsing erh chieh pʿien wei fen fang chʿeng
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注記
Translated from the Chinese by Kai Seng Chou [Kaising Tso]
Includes bibliographical references (p. 247-249)
内容説明・目次
内容説明
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.
目次
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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