Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

Messoud Efendiev (Autor)

Buch | Softcover

XVII, 258 Seiten

2019 | 1. Softcover reprint of the original 1st ed. 2018
Springer International Publishing (Verlag)
978-3-030-07491-3 (ISBN)

Artikel merken

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.

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.

"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)

Erscheinungsdatum	18.02.2019
Reihe/Serie	Fields Institute Monographs
Zusatzinfo	XVII, 258 p. 3 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	427 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Laplace Operator • Nemytskii operator • Partial differential equations • reduction of dynamics • Sobolev spaces • stabilization properties • symmetry and attractors • trajectory attractor
ISBN-10	3-030-07491-9 / 3030074919
ISBN-13	978-3-030-07491-3 / 9783030074913
Zustand	Neuware