Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 62, pp. 1-14.

Title: Sufficient conditions on diffusivity for the existence
       and nonexistence of stable equilibria with nonlinear flux 
       on the boundary

Authors: Janete Crema (USP,  S. Carlos, S. P., Brasil)
         Arnaldo Simal do Nascimento (Univ. Federal de Sao Carlos, Brasil)
	 Maicon Sonego  (Univ. Federal de Sao Carlos, Brasil)

Abstract:
 A reaction-diffusion equation with variable diffusivity and
 nonlinear flux boundary condition is considered. The goal is to
 give sufficient conditions on the diffusivity function for
 nonexistence and also for  existence of nonconstant stable
 stationary solutions. Applications are given for the main result of
 nonexistence.
 
Submitted June 27, 2011. Published April 12, 2012.
Math Subject Classifications: 35J25, 35B35, 35B36.
Key Words: Reaction-diffusion equation; stable stationary solutions;
           variable diffusivity; implicit function theorem.