Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

1. Auflage 2018
ISBN: 978-3-319-98406-3
Verlag: Springer International Publishing

Buch, Englisch, Band 36, 258 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 582 g

Reihe: Fields Institute Monographs

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.

Zielgruppe

Research

Autoren/Hrsg.

Efendiev, Messoud

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Nichtlineare Wissenschaft
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.