Critical Fujita Exponents To A Class Of Non-Newtonian Filtration Equations With Fast Diffusion

This paper deals with the initial value problem to a class of non-Newtonian fil-tration equations with fast difusion. In addition to the usual degeneracy in the non-Newtonian filtration equation with fast difusion, the equation is degenerate or singularat infinity, depending on the sign of the parameter related to the coefcient of difusion.We establish the blow-up theorems of Fujita type to get the critical exponent. In par-ticular, it is shown that the critical situation belongs to the blow-up case. In the prooffor blowing up of solutions, we determine the complicated interactions between thenonlinear difusion and the nonlinear source via a series of precise integral estimates,instead of pointwise comparisons.