Dynamic Properties of the p-Laplacian Reaction-Diffusion Equation in Multi-dimensional Space

In this paper we study the p-Laplacian reaction-diffusion equation u(t) - div(vertical bar del u vertical bar(p-2)del u) = k(t) f(u) subject to appropriate initial and boundary conditions. We show the positive solution u(x, t) exists globally, under the conditions on f, k and the boundary conduction function. It is proved that the solution blows up at finite time, for some initial data and additional energy type conditions, by establishing accurate estimates and using the Sobolev inequality in multi-dimensional space.