Nonlinear Diffusion Equations on Unbounded Fractal Domains

We investigate the nonlinear diffusion equation ∂u/∂t = u + up p > 1 on certain unbounded fractal domains, where 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 ifp > 1+2/ds , while solutions blow up if p ≤ 1 + 2/ds , where ds is the spectral dimension of the domain. We investigate smoothness and H¨older continuity of solutions when they exist