Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations. 1st ed. 2018

種類:

電子ブック

責任表示:

by Messoud Efendiev

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Efendiev, Messoud.
• SpringerLink (Online service)

シリーズ名:

Fields Institute Monographs ; 36

ISBN:

9783319984070 [3319984071]    

注記:

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. .
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.

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