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 Fujiita 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.
Chunpeng Wang. Sining Zheng. "Fujita type theorems for a class of nonlinear diffusion equations." Differential Integral Equations 26 (5/6) 555 - 570, May/June 2013. https://doi.org/10.57262/die/1363266078