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Critical Fujita exponents of degenerate and singular parabolic equations

Published online by Cambridge University Press:  12 July 2007

Chunpeng Wang  and
Sining Zheng
Chunpeng Wang
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China and Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China
Sining Zheng
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China ([email protected])
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Abstract

In this paper we investigate the critical Fujita exponent for the initial-value problem of the degenerate and singular nonlinear parabolic equation with a non-negative initial value, where p > m ≥ 1 and 0 ≤ λ1 ≤ λ2 < p(λ1 + 1) − 1. We prove that, for m < p ≤ pc = m + (2 + λ2)/(n + λ1), every non-trivial solution blows up in finite time, while, for p > pc, there exist both global and non-global solutions to the pro

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 2 , April 2006 , pp. 415 - 430
Copyright
Copyright © Royal Society of Edinburgh 2006

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