Global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology

In this paper we will focus on a parabolic degenerate system with respect to unknown functions uu and ww on a bounded domain of the two dimensional Euclidean space. This system appears as a mathematical model for some biological processes. Global existence and uniqueness of a nonnegative classical Hölder continuous solution are proved. The last part of the paper is devoted to the study of the asymptotic behavior of the solutions.