## Differential and Integral Equations

### Fujita type theorems for a class of nonlinear diffusion equations

#### Abstract

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.

#### Article information

Source
Differential Integral Equations, Volume 26, Number 5/6 (2013), 555-570.

Dates
First available in Project Euclid: 14 March 2013

https://projecteuclid.org/euclid.die/1363266078

Mathematical Reviews number (MathSciNet)
MR3086399

Zentralblatt MATH identifier
1299.35181

Subjects
Primary: 35K65, 35B33

#### Citation

Wang, Chunpeng; Zheng, Sining. Fujita type theorems for a class of nonlinear diffusion equations. Differential Integral Equations 26 (2013), no. 5/6, 555--570. https://projecteuclid.org/euclid.die/1363266078