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引用次数: 0
摘要
我们研究了无界薄域上具有乘法噪声的随机延迟 p-Laplacian 方程解的长期行为。我们首先证明了定义在((n+1)\)维无界薄域上的这些方程的有节制随机吸引子的存在性和唯一性。然后,当一个 \((n+1)\) -维薄域族退化到一个 n 维域上时,随着薄度度量趋近于零,这些吸引子的上半连续性被建立起来。
Limiting dynamics for stochastic delay p-Laplacian equation on unbounded thin domains
We study the long-term behavior of solutions for stochastic delay p-Laplacian equation with multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of tempered random attractors for these equations defined on \((n+1)\)-dimensional unbounded thin domains. Then, the upper semicontinuity of these attractors when a family of \((n+1)\)-dimensional thin domains degenerates onto an n-dimensional domain as the thinness measure approaches zero is established.
期刊介绍:
The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.