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Register a new userPullback attractors for a class of non-autonomous thermoelastic plate systems
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In this article we study the asymptotic behavior of solutions, in sense of global pullback attractors, of the evolution system $$ begin{cases} u_{tt} +etaDelta^2 u+a(t)Deltatheta=f(t,u), & t>tau, xinOmega, theta_t-kappaDelta theta-a(t)Delta u_t=0, & t>tau, xinOmega, end{cases} $$ subject to boundary conditions $$ u=Delta u=theta=0, t>tau, xinpartialOmega, $$ where $Omega$ is a bounded domain in $mathbb{R}^N$ with $Ngeqslant 2$, which boundary $partialOmega$ is assumed to be a $mathcal{C}^4$-hypersurface, $eta>0$ and $kappa>0$ are constants, $a$ is an Holder continuous function, $f$ is a dissipative nonlinearity locally Lipschitz in the second variable.
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We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L^2(R^n) and H^1(R^n), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.
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