Fujita type theorems for a class of nonlinear diffusion equations. (English) Zbl 1299.35181

Summary: This paper studies a class of weighted non-Newtonian filtration equations with slow diffusion. By using the method introduced by Galaktionov and Levine for the classical non-Newtonian filtration equation, we establish the blow-up theorems of Fujita type for the extended model, where more difficult and complicated estimates are required to treat the additional degeneracy and singularity. In particular, we prove via a delicate analysis that the critical situation of \(p=p_c\) belongs to the blow-up case. The conclusions of this paper quantitatively show the influence of the degeneracy and singularity to the critical Fujita exponents of non-Newtonian filtration equations.


35K65 Degenerate parabolic equations
35B33 Critical exponents in context of PDEs
35B44 Blow-up in context of PDEs