This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.
Contents:
- Preface
- Preliminaries
- Monotone and Accretive Operators in Banach Spaces
- Nonlinear Elliptic Boundary Value Problems
- Nonlinear Dissipative Dynamics
- Bibliography
- Index
Readership: Specialists in the theory of partial differential equations and mathematical physics. This text is recommended also for an one semester graduate course on partial differential equations.
Key Features:
- The book is self-contained and the general theory is confined to essentials necessary for the treatment of nonlinear partial differential equations
- It contains many new results which appear for the first time in a book form
