记忆型非经典扩散方程在 H1（Rn) x Lu2(R+;H1(Rn))中的全局吸引子

数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1205-1223.

记忆型非经典扩散方程在 H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ))中的全局吸引子

汪璇*(),韩英(),高承华()

西北师范大学数学与统计学院兰州 730070

收稿日期:2017-07-17 出版日期:2018-12-26 发布日期:2018-12-27
通讯作者: 汪璇 E-mail:wangxuan@nwnu.edu.cn;469328224@qq.com;gaochenghua@nwnu.edu.cn
作者简介:韩英, E-mail:469328224@qq.com|高承华, E-mail:gaochenghua@nwnu.edu.cn
基金资助:
国家自然科学基金(11761062);国家自然科学基金(11561064);国家自然科学基金(11661071);西北师范大学青年教师科研能力提升计划(NWNU-LKQN-14-6);甘肃省高校科研项目(2016A-003)

Global Attractor in H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ)) for the Nonclassical Diffusion Equations with Fading Memory

Xuan Wang*(),Ying Han(),Chenghua Gao()

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2017-07-17 Online:2018-12-26 Published:2018-12-27
Contact: Xuan Wang E-mail:wangxuan@nwnu.edu.cn;469328224@qq.com;gaochenghua@nwnu.edu.cn
Supported by:
the NSFC(11761062);the NSFC(11561064);the NSFC(11661071);the Young Teachers Scientific Research Ability Promotion Plan of Northwest Normal University(NWNU-LKQN-14-6);the Science Research Project for Colleges and Universities of Gansu Province(2016A-003)

摘要/Abstract

摘要：

该文研究了带有衰退记忆和超临界非线性项的非经典扩散方程在无界域${{\mathbb{R}}^{n}}$中的动力学行为.运用半群理论和收缩函数方法，当外力项仅属于H^-1（${{\mathbb{R}}^{n}}$）时，证明了全局吸引子在${{H}^{1}}\left( {{\mathbb{R}}^{n}} \right)\times L_{\mu }^{2}\left( {{\mathbb{R}}^{+}};{{H}^{1}}\left( {{\mathbb{R}}^{n}} \right) \right)$中的存在性.

关键词: 非经典扩散方程, 衰退记忆, 收缩函数, 全局吸引子

Abstract:

In this paper, we are concerned with the dynamical behavior of the nonclassical diffusion equations with fading memory and supercritical nonlinearity on unbounded domain ${{\mathbb{R}}^{n}}$. By applying semigroup theory and method of contractive function, we obtain the existence of global attractors in ${{H}^{1}}\left( {{\mathbb{R}}^{n}} \right)\times L_{\mu }^{2}\left( {{\mathbb{R}}^{+}};{{H}^{1}}\left( {{\mathbb{R}}^{n}} \right) \right)$, when the external forcing term g merely belongs to H^-1(${{\mathbb{R}}^{n}}$).

Key words: Nonclassical diffusion equation, Fading memory, Contractive function, Global attractor

中图分类号:

O175.8

汪璇, 韩英, 高承华. 记忆型非经典扩散方程在 H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ))中的全局吸引子[J]. 数学物理学报, 2018, 38(6): 1205-1223.

Xuan Wang, Ying Han, Chenghua Gao. Global Attractor in H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ)) for the Nonclassical Diffusion Equations with Fading Memory[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1205-1223.

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[1]	刘世芳, 马巧珍. 具有历史记忆的阻尼吊桥方程强全局吸引子的存在性[J]. 数学物理学报, 2017, 37(4): 684-697.
[2]	汪永海, 秦玉明. 非经典扩散方程的拉回吸引子在H₀¹(Ω)中的上半连续性[J]. 数学物理学报, 2016, 36(5): 946-957.
[3]	马巧珍, 徐玲, 张彦军. 记忆型非经典反应扩散方程在R³中解的渐近性态[J]. 数学物理学报, 2016, 36(1): 36-48.
[4]	张彦军, 马巧珍. 非经典反应扩散方程在R³中全局吸引子的存在性[J]. 数学物理学报, 2015, 35(2): 294-305.
[5]	马文君, 马巧珍, 高培明. 非线性弹性杆振动方程的全局吸引子及正则性[J]. 数学物理学报, 2014, 34(2): 445-453.
[6]	马巧珍;孙春友;钟承奎. 非线性梁方程强全局吸引子的存在性[J]. 数学物理学报, 2007, 27(5): 941-948.

记忆型非经典扩散方程在 H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ))中的全局吸引子

Global Attractor in H¹（Rⁿ) x L_u²(R⁺;H¹(Rⁿ)) for the Nonclassical Diffusion Equations with Fading Memory

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