Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation (Q380067)

In this paper, the authors study a parabolic-parabolic chemotaxis system in two- and three-dimensional smooth bounded domains. The problem is considered in a given region of the parameter space. They construct global bounded solutions and define a dynamical system generated by these solutions. They also derive uniform estimates for these solutions and find an absorbing ball, the radius of which is determined by a priori estimates. The existence of a global attractor and of an exponential attractor is assured by applying the existence theorem of Eden-Foias-Nicolaenko-Temam.