具有奇异振动外力项的非自治修正Swift-Hohenberg方程一致吸引子的一致有界性和收敛性  

The Uniform Boundedness and Convergence of Uniform Attractors for the Non-autonomous Modified Swift-Hohenberg Equations with Singularly Oscillating External Force

作　　者：刘世芳[1] 马巧珍[1] LIU Shifang MA Qiaozhen(College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gans)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《四川师范大学学报（自然科学版）》2016年第6期838-842,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11101334);甘肃省自然科学基金(1107RJZA223)

摘　　要：考虑当ρ∈[0,1)和ε>0时,具有奇异振动外力项的非自治修正Swift-Hohenberg(S-H)方程u_t+△~2u+2△u+au+b|▽u|~2+u^3=g(x,t)+ε^(-ρ)h(t/ε),和相应的ε=0时的S-H方程u_t+△~2u+2△u+au+b|▽u|~2+u^3=g(x,t),在外力项g∈L_b^2(R;L^2(Ω)),h∈L_n^2(R;L^2(Ω))的条件下,得到第一个方程一致吸引子A~ε的一致有界性;进一步当ε→0^+时,证明A~ε收敛到第二个方程的吸引子A^0.In this paper,we consider the non-autonomous modified Swift-Hohenberg equations with singularly oscillating external forceut＋△2u＋2△u＋au＋b｜（△）u｜2＋u3=g（x,t）＋ε-ρh（t/ε）,for ρ∈[0,1） and ε〈0,and the corresponding S-H equationut＋△2u＋2△u＋au＋b｜（△）u｜2＋u3=g（x,t）,as ε=0.When g∈L（R;L2（Ω） and h∈L（R;L2（Ω）,we obtain the uniform （w.r.t.ε） boundedness of the related uniform attractors Aε.Furthermore,the convergence of the attractors Aε of the first equation to the attractor A0 of the second one is proved as ε→0＋.

关 键 词：修正的Swift-Hohenberg方程 一致吸引子 奇异振动外力项 一致有界 

分 类 号：O175.29[理学—数学]