涉及Grushin算子的非自治抛物系统动力学

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2011-04-14 DOI:10.1155/2011/178057

Toi Vu Manh

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引用次数: 4

摘要

研究了有界区域上含Grushin算子的非自治半线性抛物型系统解的长时间行为。在一般情况下，我们证明了相应过程的回拉吸引子的存在性。当系统具有特殊的梯度结构时，我们证明了所得到的回拉吸引子更加规则，并且具有有限的分形维数。所得结果特别推广和改进了反应扩散方程和Grushin方程的一些已有结果。

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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On the Dynamics of Nonautonomous Parabolic Systems Involving the Grushin Operators

We study the long-time behavior of solutions to nonautonomous semilinear parabolic systems involving the Grushin operators in bounded domains. We prove the existence of a pullback -attractor in for the corresponding process in the general case. When the system has a special gradient structure, we prove that the obtained pullback -attractor is more regular and has a finite fractal dimension. The obtained results, in particular, extend and improve some existing ones for the reaction-diffusion equations and the Grushin equations.

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.