Differential and Integral Equations

Fujita type theorems for a class of nonlinear diffusion equations

Chunpeng Wang and Sining Zheng

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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

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

First available in Project Euclid: 14 March 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65, 35B33


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

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