Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions (Q713390)

The authors consider the following non-autonomous quasi-linear parabolic equation \[ u_t-\text{div}(|\nabla u|^{p-2}\nabla u)+f(u)=h(t), \qquad \text{in }\Omega, \] with the dynamical boundary condition \[ u_t+|\nabla u|^{p-2}\partial_n u+g(u)=0,\qquad\text{on }\Gamma \] and the initial condition \[ u(\tau)=u_\tau,\qquad\text{in }\bar\Omega, \] where \(\Omega\) is a bounded domain of \({\mathbb R}^N\) with smooth boundary \(\Gamma\), \(p\geq2\), \(h, f, g\) satisfy some conditions. By the theory of pullback attractors, the authors analyze the asymptotic behavior of the solutions of the problem.