On support of solutions to singular nonlinear parabolic equations in bounded domains

Abstract

We investigate support properties of nonnegative solutions to nonlinear parabolic equations with variable density in bounded domains. The density can diverge or vanish near the boundary. Assuming that the initial datum has support not intersecting the boundary, we provide simple conditions, in dependence on the behaviour of the density, guaranteeing that the support of every nonnegative solution intersects the boundary at some positive time, or, in the case of convex domains, that it remains away from it for any positive time. These results extend to the case of bounded domains those given in [KK] for the Cauchy problem.