非自治Kuramoto-Sivashinsky方程一致吸引子的存在性、一致有界性和收敛性  

Existence,uniform boundedness and convergence of uniform attractors for the non-autonomous Kuramoto-Sivashinsky equations

作　　者：沈晓鹰 马巧珍[1] 

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《华中师范大学学报（自然科学版）》2016年第2期168-173,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11101334);甘肃省自然科学基金项目(1107RJZA223);甘肃省教育厅高校科研业务费项目

摘　　要：讨论了具有奇异振动外力项的Kuramoto-Sivashinsky方程ut+Δ2 u+Δu+u·▽u=g(x,t)+ε-ρh(t/ε),u|t=τ=uτ和相应的Kuramoto-Sivashinsky方程ut+Δ2 u+Δu+u·▽u=g(x,t),u|t=τ=uτ在外力项g(x,t),h(x,t/ε)仅满足平移有界而非平移紧时H2per空间中一致吸引子Aε的存在性,进一步证明了第一个方程的一致吸引子Aε的一致有界性,并且,当ε→0+时,Aε收敛到第二个方程的吸引子A0.In this paper,the existence of uniform attractors Aεis proved in the space H2 per when the external force terms satisfy the bounded transition instead of transition impact within the non-autonomous Kuramoto-Sivashinsky equation：ut＋Δ2u ＋Δu＋u·▽u=g（x,t）＋ε-ρh（t/ε）,u｜t=τ=uτ for ρ∈[0,1]and ε0 and the corresponding K-S equation：ut＋Δ2u ＋Δu＋u·▽u=g（x,t）,u｜t=τ=uτ,asε=0.Furthermore,the uniform（w.r.t.ε）boundedness of a class of uniform attractors Aεare verified as well as the convergence of the attractors Aεfor the first equation to the attractor A0 of the second one asε→0＋.

关 键 词：KURAMOTO-SIVASHINSKY方程 一致吸引子 一致有界性 收敛性 

分 类 号：O175.29[理学—数学]