Partial symmetries of solutions to nonlinear elliptic and parabolic problems in bounded radial domains
- We consider a class of nonautonomous nonlinear competitive parabolic systems on bounded radial domains under Neumann or Dirichlet boundary conditions. We show that, if the initial profiles satisfy a reflection inequality with respect to a hyperplane, then bounded positive solutions are asymptotically (in time) foliated Schwarz symmetric with respect to antipodal points. Additionally, a related result for (positive and sign changing solutions) of scalar equations with Neumann or Dirichlet boundary conditions is given. The asymptotic shape of solutions to cooperative systems is also discussed.
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| Author: | Alberto Saldaña de FuentesORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-344219 |
| Publisher: | Univ.-Bibliothek |
| Place of publication: | Frankfurt am Main |
| Referee: | Tobias WethORCiDGND, Nils Ackermann |
| Advisor: | Tobias Weth |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2014/07/03 |
| Year of first Publication: | 2014 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Granting Institution: | Johann Wolfgang Goethe-Universität |
| Date of final exam: | 2014/07/02 |
| Release Date: | 2014/07/10 |
| Tag: | Lotka-Volterra system; cooperative systems; foliated Schwarz symmetry; rotating plane method |
| Page Number: | 126 |
| HeBIS-PPN: | 343114054 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Deutsches Urheberrecht |
