Unbounded attractor of a quasilinear parabolic equation (Q580588)

Let \(\Omega\) be a bounded domain in \(R^ n\) with smooth boundary \(\partial \Omega\), \(Q_ T=\Omega \times]0,T[\), \(S_ t\) be the semigroup corresponding to the following boundary value problem in \(Q_ T\) \[ u_ t=\Delta u+\lambda u+f(u),\quad u|_{\partial \Omega \times]0,T[}=0,\quad u|_{t=0}=u_ 0(x), \] where \(f: R\to R\), \(f(u)\in C^ 1(R)\), \(| f(u)| \leq C\), \(| f'(u)| \leq C\), f(u)\(\to 0\) (\(| u| \to \infty)\), \(u_ 0(x)\in L_ 2(\Omega).\) The author announces the existence of a maximal attractor of \(S_ t\) and gives its structure.