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.

Reviews

"Serves as a good introduction for postgraduate students ... For advanced researchers, it is also a good reference to many useful results and to various kinds of techniques."

-- Bulletin of the London Mathematical Society

"A well-written and instructive collection of recent results on various topics in the field of nonlinear second-order PDEs ... the exposition is exceptionally clear; Tso has provided a competent and very readable translation."

-- Mathematical Reviews

"Clearly written, its global quality is good."

-- Zentralblatt MATH

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 Schrödinger 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)
• Symbols
• References