具有整体空间记忆的退化抛物方程的动力学行为

IF 1.7 4区 数学 Q1 Mathematics
Rong Guo, Xuan Leng
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引用次数: 0

摘要

本文关注的是一类在 $\mathbb{R}^{n}$ 上有记忆的退化抛物方程的全局吸引子的存在性和唯一性。由于相应方程包含退化项 $\operatorname{div}\{a(x)\nabla u\}$ ,这就要求我们在研究问题时对权重函数 $a(x)$ 给出适当的假设。在此基础上,我们首先得到了有界吸收集的存在性,然后通过渐近收缩半群法验证了解半群的渐近紧凑性。最后,证明了全局吸引子的存在性和唯一性。特别是,非线性 f 满足任意阶 $p-1$ ($p\geq 2$)的多项式增长,并采用解的均匀尾估计的思想来证明解的强收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamical behavior of a degenerate parabolic equation with memory on the whole space
This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on $\mathbb{R}^{n}$ . Since the corresponding equation includes the degenerate term $\operatorname{div}\{a(x)\nabla u\}$ , it requires us to give appropriate assumptions about the weight function $a(x)$ for studying our problem. Based on this, we first obtain the existence of a bounded absorbing set, then verify the asymptotic compactness of a solution semigroup via the asymptotic contractive semigroup method. Finally, the existence and uniqueness of global attractors are proved. In particular, the nonlinearity f satisfies the polynomial growth of arbitrary order $p-1$ ( $p\geq 2$ ) and the idea of uniform tail-estimates of solutions is employed to show the strong convergence of solutions.
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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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