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Nonlinear Second-Order Partial Differential Equations
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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 which 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 particula...
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 which 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 an invaluable 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).
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).