Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation

Abstract

We construct the global bounded solutions and the attractors of a parabolic-parabolic chemotaxis-growth system in two- and three-dimensional smooth bounded domains We derive new Lp and H2 uniform estimates for these solutions We then construct the absorbing sets and the global attractors for the dynamical systems generated by the solutions We also show the existence of exponential attractors by applying the existence theorem of Eden- Foias-Nicolaenko-Temam.