Quasilinear abstract parabolic evolution equations and exponential attractors

Abstract

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