Asymptotic structure of the attractor for processes on time-dependent spaces

Abstract

We compare the asymptotic structure of the time-dependent attractor At generated by the partial differential equation εutt+αut−Δu+f(u)=g, where the positive function ε=ε(t) tends to zero as t→∞, with the global attractor A∞ of its formal limit αut−Δu+f(u)=g. We establish an abstract result and we apply it to the proof of the convergence At→A∞.