A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach Progress in Nonlinear Differential Equations and Their Applications

This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of nonlinear diffusion equations. The underlying theory hinges on a new stability result, formulated in the abstract setting of infinite-dimensional dynamical systems, which states that under certain hypotheses, the omega-limit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations.

The Stability Theorem is examined in detail in the first chapter, followed by a review of basic results and methods-many original to the authors-for the solution of nonlinear diffusion equations.