On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems

Abstract

Some nonlinear stationary reaction-diffusion systems involving nonlinear terms which may be discontinuous are considered. Such systems occur, for instance, in the study of chemical reactions, and the discontinuities correspond to reactions of order zero. In such concrete models, the set where the reactant vanishes plays an important role. Here we prove the existence of solutions for a general class of such systems satisfying Dirichlet or nonlinear boundary conditions. Necessary and sufficient conditions are given assuring that the reactant component vanishes on a set of positive measure. Estimates on the location of such set are given.