Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors (Q2847034)

This paper deals with a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors. The model includes two elliptic equations describing the concentration of nutrients and inhibitors, respectively, and a Stokes equation for the fluid velocity and internal pressure. The authors convert the problem with free boundary into an initial-boundary value problem on a fixed domain. Then, the Cauchy problem of an abstract differential equation in a Banach space is investigated. The main result is the stability and the instability of stationary solutions depending on the data of the problem.