Rn上Plate方程全局吸引子的正则性和有限维性

基金项目: 浙江省教育厅科研基金资助项目(Y200804289);宁波市自然科学基金资助项目(2010A610102);宁波大学王宽存基金的资助

Regularity and Finite Dimensionality of Attractor for Plate Equation on Rⁿ

Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P. R. China;

摘要: 研究了无界区域Rn上Plate方程全局吸引子的正则性和有限分形维性.该方程的全局吸引子在相空间H2(Rn)×L2(Rn)的存在性已在先期文章建立,现在进一步证明该全局吸引子具有更好的正则性，即它是H4(Rn)×H2(Rn)的有界集并具有有限分形维数．
- 全局吸引子 /
- Plate方程 /
- 正则性 /
- 有限维性 /
- 无界区域
Abstract: Regularity and finite dimensionality of global attractor for plate equation on unbounded domain Rⁿ were studied. Existence of the attractor inphase space H²(Rⁿ)×L² (Rⁿ) was established in the author's earlier paper. It is showed that the attractor is actually a bounded set of H⁴ (Rⁿ)×H²(Rⁿ) and has finite fractal dimensionality.
- global attractor /
- Plate equation /
- regularity /
- finite dimensionality /
- unbounded domain

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