Pullback attractors for a singularly nonautonomous plate equation

We consider the family of singularly nonautonomous plate equation with structural damping $$u_{tt} + a(t,x)u_{t} + (- \Delta) u_{t} + (-\Delta)^{2} u + \lambda u = f(u),$$ in a bounded domain $\Omega \subset \R^n$, with Navier boundary conditions. When the nonlinearity $f$ is dissipative we show that this problem is globally well posed in $H^2_0(\Omega) \times L^2(\Omega)$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$

Continuity of attrators for semilinear parabolic problems with localized large diffusion

Neste trabalho estudamos comportamento assintótico de problemas parabólicos semilineares do tipo ut ¡div(p(x)Nu)+l u = h(u) em um domí?nio limitado e suave W ½ Rn, com condições de Neumann na fronteira, quando o coeficiente de difusão p se torna grande em uma sub-região W0 que é interior ao domí?nio físico W. Provamos que, sob determinadas hipóteses, a família de atratores se comporta semicontinuamente inferior e superiormente quando a difusão explode em W0In this work we study the asymptotic behavior of semilinear parabolic problems of the form ut ¡div(p(x)Ñu)+l u = h(u) in a bounded smooth domain W ½ Rn and Neumann boundary conditions when the diffusion coefficient p becomes large in a subregion W0 which is interior to the physical domain W. We prove, under suitable assumptions, that the family of attractors behave upper and lowersemicontinuously as the diffusion blows up in W0

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved