Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

 
 
Springer (Verlag)
  • erschienen am 26. Oktober 2018
 
  • Buch
  • |
  • Hardcover
  • |
  • XVII, 258 Seiten
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.
Book
1st ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 3 s/w Abbildungen
  • |
  • Bibliographie
  • Höhe: 245 mm
  • |
  • Breite: 164 mm
  • |
  • Dicke: 22 mm
  • 569 gr
978-3-319-98406-3 (9783319984063)
10.1007/978-3-319-98407-0
weitere Ausgaben werden ermittelt
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.

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