Electron. J. Diff. Equ., Vol. 2011 (2011), No. 77, pp. 1-13.

Pullback attractors for a singularly nonautonomous plate equation

Vera Lucia Carbone, Marcelo Jose Dias Nascimento, Karina Schiabel-Silva, Ricardo Parreira da Silva

Abstract: We consider the family of singularly nonautonomous plate equations with structural damping
$$ u_{tt} + a(t,x)u_t - \Delta u_t + (-\Delta)^2 u + \lambda u = f(u), $$
in a bounded domain $\Omega \subset \mathbb{R}^n$, 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.

Submitted January 14, 2011. Published June 20, 2011.
Math Subject Classifications: 35B41, 35L25, 35Q35.
Key Words: Pullback attractor; nonautonomous system; plate equation; upper-semicontinuity.

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Vera Lúcia Carbone
Departamento de Matemática
Universidade Federal de São Carlos
13565-905 Sãao Carlos SP, Brazil
email: carbone@dm.ufscar.br
  Marcelo José Dias Nascimento
Departamento de Matemática, Universidade Federal de São Carlos
13565-905 Sãao Carlos SP, Brazil
email: marcelo@dm.ufscar.br
  Karina Schiabel-Silva
Departamento de Matemática, Universidade Federal de São Carlos
13565-905 Sãao Carlos SP, Brazil
email: schiabel@dm.ufscar.br
Ricardo Parreira da Silva
Departamento de Matemática
IGCE-UNESP, Caixa Postal 178
13506-700 Rio Claro SP, Brazil
email: rpsilva@rc.unesp.br

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