| 汪璇,居文超,钟承奎.具有衰退记忆的非自治非经典扩散方程的强吸引子[J].数学年刊A辑,2013,34(6):671~688 |
| 具有衰退记忆的非自治非经典扩散方程的强吸引子 |
| Strong Attractors for the Non-autonomous Nonclassical Diffusion Equations withFading Memory |
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| DOI： |
| 中文关键词: 非经典扩散方程, 一致吸引子,
临界指数, 渐近正则性, 衰退记忆 |
| 英文关键词:Nonclassical diffusion equation, Uniform attractor,
Critical exponent, Asymptotic regularity, Fading memory |
| 基金项目:国家自然科学基金 (No.11101134, No.11361053)和西北师范大学青年教师科研能力提升计划项目(No.NWNU-LKQN-11-5) |
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| 中文摘要: |
| 在强拓扑空间$H_0^1(\Omega)\cap
H^2(\Omega)$$\times L_\mu^2(\mathbb R^+; H_0^1(\Omega)\cap
H^2(\Omega))$中, 讨论了具有衰退记忆的非自治非经典扩散方程
当非线性项临界增长时的长时间动力学行为. 当与时间相关的外力项
仅满足平移有界而非
平移紧时, 首先
得到了强解的渐近正则性, 然后获得了强吸引子的存在性及其结构与正则性.
该结果推广和改进了一些已有结果. |
| 英文摘要: |
| The authors discuss the long-time dynamical behavior of the
non-autonomous nonclassical diffusion equation with fading memory
in the strong topological space $H_0^1(\Omega)\cap
H^2(\Omega)$$\times L_\mu^2(\mathbb R^+; H_0^1(\Omega)\cap
H^2(\Omega))$ when nonlinearity is critical. At first the asymptotic
regularity of strong solutions is obtained, and then the existence
of a compact uniform attractor together with its structure and
regularity is obtained, while the time-dependent forcing term is only
translation bounded instead of translation compact. The result
extends and improves some known results. |
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