New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms

This paper deals with the new Fujita type results for Cauchy problem of a quasilinear parabolic differential inequality with both a source term and a gradient dissipation term. Specially, nonnegative weights may be singular or degenerate. Under the assumption of slow decay on initial data, we prove...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 11482 - 11493
Main Authors Wang, Xiaomin, Fang, Zhong Bo
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
global solutions
nonexistence of solutions
parabolic differential inequalities
second critical exponent
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Summary:This paper deals with the new Fujita type results for Cauchy problem of a quasilinear parabolic differential inequality with both a source term and a gradient dissipation term. Specially, nonnegative weights may be singular or degenerate. Under the assumption of slow decay on initial data, we prove the existence of second critical exponents $ \mu^{*} $, such that the nonexistence of solutions for the inequality occurs when $ \mu < \mu^{*} $.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021665