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

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 93-100.

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

李仲庆()

贵州财经大学数学与统计学院贵阳 550025

收稿日期:2022-09-06 修回日期:2023-09-11 出版日期:2024-02-26 发布日期:2024-01-10
作者简介:李仲庆, E-mail：zqli_jlu@163.com
基金资助:
国家自然科学基金(11901131);2022年度贵州财经大学校级项目(2022KYYB01)

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

Li Zhongqing()

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025

Received:2022-09-06 Revised:2023-09-11 Online:2024-02-26 Published:2024-01-10
Supported by:
NSFC(11901131);University-level Research Fund Project in Guizhou University of Finance and Economics(2022KYYB01)

摘要/Abstract

摘要：

该文主要证明了一类具变指数的抛物方程解的存在性结果.虽然源项的可积性不高, 但是, 零阶项产生的正则化效应帮助得到了$L^\infty$估计. 通过选取合适的检验函数, 得到了逼近解序列$\{u^\epsilon\}_\varepsilon$必要的先验估计. 运用 Young 测度方法, 确定了非线性项的弱收敛元.

关键词: 变指数, 零阶项, Young 测度

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

中图分类号:

O175.8

李仲庆. 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[J]. 数学物理学报, 2024, 44(1): 93-100.

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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