带记忆项半线性反应扩散方程的强吸引子  

Strong Attractors for Semilinear Reactiondiffusion Equations with Memory

作　　者：唐志飘 孙春友[2] 谢永钦 Tang Zhipiao;Sun Chunyou;Xie Yongqin(School of General Education Hunan University of Information Technology,Changsha 410151,China;School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China)

机构地区：[1]湖南信息学院通识教育学院,长沙410151 [2]兰州大学数学与统计学院,兰州730000

出　　处：《数学理论与应用》2023年第1期115-125,共11页Mathematical Theory and Applications

基　　金：湖南省自然科学基金(No.2022JJ30417);湖南省研究生科研创新项目(No.CX20200891)资助。

摘　　要：本文讨论带衰退记忆项的非线性反应扩散方程整体强解的长时间行为.首先,利用控制收敛原理及解的正则性证明系统解半群为积空间H^(1)_(0)(Ω)×L^(2)_(μ)(R;D(A))上的压缩半群,由此得到解半群的渐近紧性;然后,证明积空间上全局吸引子A的存在性和正则性.值得注意的是非线性项f满足任意阶多项式增长条件,并且A⊂D(A)×L^(2)_(μ)(R;D(A)).In this paper,we discuss the long time behavior of strong solutions of semilinear reaction diffusion equations with fading memory.First of all,by the regularity of solutions and the control convergence principle,we prove that the semigroup of the solutions is an contractive semigroup on H^(1)_(0)(Ω)×L^(2)_(μ)(R;D(A)),which leads to the asymptotic compactness of the semigroup.Then,we show the existence and regularity of global attractor A on the product space.It is noteworthy that the nonlinearity f satisfies the polynomial growth of arbitrary order and A⊂D(A)×L^(2)_(μ)(R;D(A)).

关 键 词：反应扩散方程 控制收敛原理 压缩半群 任意阶多项式增长 全局吸引子 

分 类 号：O175[理学—数学]