一类具p(·,·)结构和L^(1)源的非线性抛物方程解的存在性  

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

作　　者：李仲庆 Li Zhongqing(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025

出　　处：《数学物理学报（A辑）》2024年第1期93-100,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11901131);2022年度贵州财经大学校级项目(2022KYYB01)。

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^(∞)估计.通过选取合适的检验函数,得到了逼近解序列{u^(ε)}ε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.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 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^(ε)}ε.Thanks to the Young measure method,the weak convergence of the nonlinear term is identified.

关 键 词：变指数 零阶项 Young测度 

分 类 号：O175.8[理学—数学]