Pullback attractors for a singularly nonautonomous plate equation
Abstract
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 uppersemicontinuous under small perturbations of the damping $a$.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 arXiv:
 arXiv:1012.4749
 Bibcode:
 2010arXiv1012.4749L
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 Electronic Journal of Differential Equations n{\deg} 77, (2011), pp 113