Nonlinear Diffusion Equations on Unbounded Fractal Domains

We investigate the nonlinear diffusion equation partial derivativeu/partial derivativet Deltau + up, p > 1, on certain unbounded fractal domains, where Delta is the infinitesimal generator of the semigroup associated with a corresponding heat kernel. We show that there are nonnegative global solutions for non-negative initial data if p > If 2/d(s), while solutions blow up if p less than or equal to 1 + 2/d(s), where d(s) is the spectral dimension of the domain. We investigate smoothness and Holder continuity of solutions when they exist. (C) 2001 Academic Press.