TY  - BOOK
AU  - Efendiev,Messoud
TI  - Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations
T2  - Fields Institute Monographs
SN  - 3319984071
U1  - 515.353 23
PY  - 2018///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Partial differential equations
KW  - Dynamics
KW  - Ergodic theory
N1  - Bibliography: pages 253-258; 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
N2  - 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
ER  -