TITLE:
On the existence of patterns for a diffusion equation on a convex
domain with nonlinear boundary reaction
AUTHORS:
Neus Consul (1) and Angel Jorba (2)
(1) Departament de Matematica Aplicada I,
Universitat Politecnica de Catalunya,
Diagonal 647, 08028 Barcelona, Spain.
E-mail: neus.consul@upc.es
(2) Departament de Matematica Aplicada i Analisi,
Universitat de Barcelona,
Gran Via 585, 08007 Barcelona, Spain.
E-mail: angel@maia.ub.es
ABSTRACT:
We consider a diffusion equation on a domain $\Omega$ with a cubic
reaction at the boundary. It is known that there are no patterns when
the domain $\Omega$ is a ball, but the existence of such patterns is
still unkown in the more general case in which $\Omega$ is convex.
The goal of this paper is to present numerical evidence of the
existence of nonconstant stable equilibria when $\Omega$ is the unit
square. These patterns are found by continuation of families of
unstable equilibria that bifurcate from constant solutions.