Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

被引:33
作者
Bruschi, S. M.
Carvalho, A. N.
Cholewa, J. W.
Dlotko, Tornasz
机构
[1] UNESP, Dept Matemat, IGCE, BR-13506700 Rio Claro, SP, Brazil
[2] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computac, BR-13560970 Sao Carlos, SP, Brazil
[3] Silesian Univ, Inst Math, PL-40007 Katowice, Poland
关键词
damped wave equation; strongly damped wave equation; dissipative semigroup; global attractor; uniform exponential dichotomy; upper; semicontinuity; lower semicontinuity;
D O I
10.1007/s10884-006-9023-4
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).
引用
收藏
页码:767 / 814
页数:48
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