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 $.
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 $.
Pullback attractors for a singularly nonautonomous plate equation
V Lúcia Carbone, M José Dias Nascimento… - arXiv e …, 2010 - ui.adsabs.harvard.edu
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 $.
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 $.
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