Global attractors for quasilinear parabolic equations on unbounded thin domains
The author deals with the asymptotic behavior of a class of quasi-linear equations defined in an unbounded domain \(\Omega \subseteq \mathbb{R}^{n+1}\): \[ u_t -\Delta _p u + a(x,y) |u|^{p-2} u =f(u), \quad \text{in} \;\Omega, \] \[ {\frac {\partial u}{\partial n}} =0 \quad \text{ on } \;\partial \Omega, \] where \(\Delta_p =\operatorname{div} (|\nabla u|^{p-2} \nabla u)\) with \(2 < p < n\). Under certain conditions, the existence and upper semi-continuity of global attractors for the equations are proved when the \((n +1)\)-dimensional thin domain \(\Omega\) collapses to the entire space \(\mathbb{R}^n\).
scientific article; zbMATH DE number 6608243