时变域上半线性热方程的连续性和回拉吸引子

IF 1.7 4区 数学 Q1 Mathematics
Mingli Hong, Feng Zhou, Chunyou Sun
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引用次数: 0

摘要

我们考虑的是一个半线性热方程在时变域上的动力学问题,该方程具有较低的规则强迫项。我们不要求强制项 $f(\cdot )$ 满足 $\int _{-\infty}^{t}e^{\lambda s}\|f(s)\|^{2}_{L^{2}}\,ds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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Continuity and pullback attractors for a semilinear heat equation on time-varying domains
We consider dynamics of a semilinear heat equation on time-varying domains with lower regular forcing term. Instead of requiring the forcing term $f(\cdot )$ to satisfy $\int _{-\infty}^{t}e^{\lambda s}\|f(s)\|^{2}_{L^{2}}\,ds<\infty $ for all $t\in \mathbb{R}$ , we show that the solutions of a semilinear heat equation on time-varying domains are continuous with respect to initial data in $H^{1}$ topology and the usual $(L^{2},L^{2})$ pullback $\mathscr{D}_{\lambda}$ -attractor indeed can attract in the $H^{1}$ -norm, provided that $\int _{-\infty}^{t}e^{\lambda s}\|f(s)\|^{2}_{H^{-1}(\mathcal{O}_{s})}\,ds< \infty $ and $f\in L^{2}_{\mathrm{loc}}(\mathbb{R},L^{2}(\mathcal{O}_{s}))$ .
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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