ASYMPTOTIC BEHAVIOR OF GLOBAL SOLUTIONS TO A MODEL OF CELL INVASION

In this paper, we analyze a mathematical model focusing on key events of the cell invasion process. The three equations of the corresponding coupled system describe the behavior of the invasive cells, the extracellular matrix and the degradative enzymes. We employ a fix-point method and a priori estimates to prove local and global existence, uniqueness and regularity properties of the solutions. Our approach enable us to find estimates that are uniform in time. This is essential in proving, in the last part of the paper, new results that establish the asymptotic behavior of the solutions.