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^{*} $.
Citation: Xiaomin Wang, Zhong Bo Fang. New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms[J]. AIMS Mathematics, 2021, 6(10): 11482-11493. doi: 10.3934/math.2021665
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^{*} $.
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Xiaomin Wang, Zhong Bo Fang. New Fujita type results for quasilinear parabolic differential inequalities with gradient dissipation terms[J]. AIMS Mathematics, 2021, 6(10): 11482-11493. doi: 10.3934/math.2021665
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