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.