Extinction and positivity for a system of semilinear parabolic variational inequalities

Abstract

A simple model of chemical kinetics with two concentrations u and v can be formulated as a system of two parabolic variational inequalities with reaction rates v(p) and u(q) for te diffusion processes of u and v, respectively. It is shown that if pq < 1 and the initial values of u and v are “comparable” then at least one of the concentrations becomes extinct in finite time. On the other hand, for any p = q > 0 there are initial values for which both concentrations do not become extinct in any finite time.