一类带对数非线性项的抛物方程解的存在性和爆破

Abstract

Abstract:

In this paper, we consider the initial boundary value problem of a viscoelastic equation with logarithmic nonlinearity. Under some suitable conditions, we obtain the existence of global weak solutions. Otherwise, we get that the solution does not blow up in any finite time. This is different from the situation of the viscoelastic equation with a polynomial nonlinearity, in which case the solution blows up in finite time.

Key words: Logarithmic nonlinearity, Viscoelastic term, Global existence, Blow-up

CLC Number:

O175

Yuge Du,Shuying Tian. Existence and Blow-Up of a Parabolic Equation with Logarithmic Nonlinearity[J].Acta mathematica scientia,Series A, 2021, 41(6): 1816-1829.

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References 18

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Existence and Blow-Up of a Parabolic Equation with Logarithmic Nonlinearity

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