Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

by Messoud Efendiev

Overview

This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.

Product Details

ISBN-13:	9783319984063
Publisher:	Springer International Publishing
Publication date:	10/18/2018
Series:	Fields Institute Monographs , #36
Edition description:	1st ed. 2018
Pages:	258
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Preface.- 1. Preliminaries.- 2. Trajectory dynamical systems and their attractors.- 3. Symmetry and attractors: the case N ≤ 3.- 4. Symmetry and attractors: the case N ≤ 4.- 5. Symmetry and attractors.- 6. Symmetry and attractors: arbitrary dimension.- 7. The case of p-Laplacian operator.- Bibliography.

Editorial Reviews

The author does a very good job with the difficult and somewhat unexpected task of pairing together elliptic PDE’s with dynamical systems methods specific to finite dimensions.” (Florin Catrina, zbMATH 1445.35005, 2020)

From the Publisher