一类具$p(\cdot,\cdot)$结构和$L^1$源的非线性抛物方程解的存在性

Abstract

Abstract:

This paper is devoted to proving an existence result to a class of nonlinear parabolic equations with variable exponents. The zero order term produces a regularizing effect, which helps to get the$L^\infty$estimate despite the poor summability of the source term. By choosing some appropriate test functions, we obtain the necessary a priori estimates for the approximate solution sequences denoted by$\{u^\epsilon\}_\varepsilon$. Thanks to the Young measure method, the weak convergence of the nonlinear term is identified.

Key words: Variable exponents, Zero order term, Young measure

CLC Number:

O175.8

Li Zhongqing. Existence Result for a Class of Nonlinear Parabolic Equations with$p(\cdot,\cdot)$Structure and an$L^1$Source[J].Acta mathematica scientia,Series A, 2024, 44(1): 93-100.

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References 17

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Existence Result for a Class of Nonlinear Parabolic Equations with$p(\cdot,\cdot)$Structure and an$L^1$Source

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