变指数时变Lebesgue空间上的演化方程

IF 0.8 4区数学 Q2 MATHEMATICS Electronic Journal of Differential Equations Pub Date : 2023-07-24 DOI:10.58997/ejde.2023.50

J. Simsen

引用次数: 0

摘要

我们将Kloeden-Simsen [CPAA 2014]中的结果推广到$p(x,t)$ -拉普拉斯问题上的变指数时变Lebesgue空间。研究了在$\mathbb{R}^n$, $n\geq 1$中有界光滑域$\Omega$上的方程$$\displaylines{ \frac{\partial u_\lambda}{\partial t}(t)-\operatorname{div}\big(D_\lambda(t,x)|\nabla u_\lambda(t)|^{p(x,t)-2}\nabla _\lambda(t)\big)+|u_\lambda(t)|^{p(x,t)-2}u_\lambda(t) =B(t,u_\lambda(t)) }$$，该方程具有齐次Neumann边界条件，其中指数$p(\cdot)\in C(\bar{\Omega}\times [\tau,T],\mathbb{R}^+)$满足$\min p(x,t)>2$, $\lambda\in [0,\infty)$是一个参数。欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/50/abstr.html

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Evolution equations on time-dependent Lebesgue spaces with variable exponents

We extend the results in Kloeden-Simsen [CPAA 2014] to $p(x,t)$-Laplacian problems on time-dependent Lebesgue spaces withvariable exponents. We study the equation $$\displaylines{ \frac{\partial u_\lambda}{\partial t}(t)-\operatorname{div}\big(D_\lambda(t,x)|\nabla u_\lambda(t)|^{p(x,t)-2}\nabla _\lambda(t)\big)+|u_\lambda(t)|^{p(x,t)-2}u_\lambda(t) =B(t,u_\lambda(t)) }$$on a bounded smooth domain $\Omega$ in $\mathbb{R}^n$,$n\geq 1$, with a homogeneous Neumann boundary condition, where the exponent $p(\cdot)\in C(\bar{\Omega}\times [\tau,T],\mathbb{R}^+)$ satisfies $\min p(x,t)>2$, and $\lambda\in [0,\infty)$ is a parameter. For more information see https://ejde.math.txstate.edu/Volumes/2023/50/abstr.html

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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.