| 汪璇,段奋霞,马群,杨光.带衰退记忆的经典反应扩散方程的强全局吸引子*[J].数学年刊A辑,2015,36(3):265~276 |
| 带衰退记忆的经典反应扩散方程的强全局吸引子* |
| Strong Global Attractors for the Classical ReactionDiffusion Equations with Fading Memory |
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| DOI： |
| 中文关键词: 经典反应扩散方程, 强全局吸引子, 任意阶多项式增长, 衰退记忆 |
| 英文关键词:Classical reaction diffusion equations, Strong global attractor,
Polynomial growth of arbitrary order, Fading memory |
| 基金项目:本文受到甘肃省自然科学基金(No.\,145RJZA112)和国家自然科学基金 (No.11361053, No.11201204, No.11261053) 的资助. |
| Author Name | Affiliation | E-mail | | WANG Xuan | College of Mathematics and Statistics, Northwest Normal University, Lanzhou
730070, China. | wangxuan@nwnu.edu.cn | | DUAN Fenxia | College of Mathematics and Statistics, Northwest Normal University, Lanzhou
730070, China. | 980866580@qq.com | | MA Qun | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China. | 1120354557@qq.com | | YANG Guang | School of Economics and Management, Lanzhou University of Technology,
Lanzhou 730050, China. | 305683617@qq.com |
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| 中文摘要: |
| 当任意阶多项式增长的非线性项为耗散, 且外力项仅属于$L^2(\Omega)$时,
研究了带衰退记忆的经典反应扩散方程的解在强拓扑空间$H_0^1(\Omega)$$\times L_\mu^2(\mathbb R^+;
D(A))$的长时间行为. 应用抽象函数理论、半群理论以及
新的估计技巧, 在拓扑空间$H_0^1(\Omega)\times L_\mu^2(\mathbb R^+;
D(A))$上, 验证了强解半群的渐近紧性并且证明了强全局吸引子的存在性. |
| 英文摘要: |
| This paper deals with the long-time behavior of solutions for the classical re-
action diffusion equations with fading memory in the strong topological space H1
0 (
) ×
L2
μ(R+;D(A)), where the nonlinearity with polynomial growth of arbitrary order is dissipa-
tive, and the forcing term only belongs to L2(
). Applying the abstract function theory, the
semigroup theory and some new estimate techniques, the authors prove the asymptotic com-
pactness of solutions and obtain the existence of global attractor in the strong topological
space H1
0 (
)×L2
μ(R+;D(A)). |
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