Publicação: Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations
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Springer
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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(+).
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damped wave equation, strongly damped wave equation, dissipative semigroup, global attractor, uniform exponential dichotomy, upper, semicontinuity, lower semicontinuity
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Inglês
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Journal of Dynamics and Differential Equations. New York: Springer, v. 18, n. 3, p. 767-814, 2006.
