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 Fuentes
Place of publication:Frankfurt am Main
Referee:Tobias WethORCiDGND, Nils Ackermann
Advisor:Tobias Weth
Document Type:Doctoral Thesis
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
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht