Multiple Solutions in Reaction-Diffusion Systems with a Free Boundary
Françis Conrad, Naji Yebari · SIAM Journal on Applied Mathematics · 1989
This paper is concerned with a simple model of the dissolution-growth process of a solid particle (grain) in an aqueous medium in the stationary case. The resulting nonlinear eigenvalue problem consists of a reaction-diffusion equation in the aqueous medium limited by an interface which is itself unknown. The various types of bifurcation diagrams according to the nonlinear reaction term are described here. Generally, more than one solution exists. Specifically, turning points, bifurcation points, or “transition” points may appear. The associated evolution problem will be investigated in the future.