02055nam a22002655i 4500 u4935 SIRSI 20250825175020.0 181017s2018 gw r 000|0 eng c 3319984071 515.353 23 Efendiev, Messoud, author. Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations / by Messoud Efendiev. 1st edition 2018. Cham : Springer International Publishing : Imprint: Springer, 2018. xvii, 258 pages. Fields Institute Monographs ; 36 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. 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. Partial differential equations. Dynamics. Ergodic theory. Fields Institute Monographs ; 36 3498 3498 2026-03-12 00:00:00 35672001096 515.353 E271s 2018 35672001096 1 2025-08-25 BOOK 0 0 0 COL_GRAL 0 BCENTRAL BCENTRAL 2023-10-02