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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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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Abstract 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^{*} $.
AbstractList 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^{*} $.
Author Wang, Xiaomin
Fang, Zhong Bo
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10.1007/BF02761845
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10.1016/j.na.2008.12.018
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10.1007/s00033-013-0337-x
10.1007/s00033-018-1046-2
10.1090/S0002-9947-1992-1057781-6
10.1016/j.mcm.2011.12.036
10.3792/pja/1195519254
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SubjectTerms global solutions
nonexistence of solutions
parabolic differential inequalities
second critical exponent
Title New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms
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