Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations
Seiten
2018
|
1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-98406-3 (ISBN)
Springer International Publishing (Verlag)
978-3-319-98406-3 (ISBN)
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 | 20.10.2018 |
|---|---|
| Reihe/Serie | Fields Institute Monographs |
| Zusatzinfo | XVII, 258 p. 3 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 578 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 | 3-319-98406-3 / 3319984063 |
| ISBN-13 | 978-3-319-98406-3 / 9783319984063 |
| Zustand | Neuware |
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