Quasilinear abstract parabolic evolution equations and exponential attractors

Abstract

The Exponential attractor, one of notions of limit set in infinite-dimensional dynamical systems, is known to have strong robustness and is known to be constructed under a simple compact smoothing condition. In this paper, we study a dynamical system determined from the Cauchy problem for a quasilinear abstract parabolic evolution equation. We give a general strategy for constructing the exponential attractor and apply the abstract result to a chemotaxis-growth system in non smooth domain.