| Abstract: |
| S.M. Wise et al. proposed a continuous mixture model for tumor growth [J. Theor. Biology 253 (2008), 524-543]. This model consists of four advective Cahn-Hilliard equations with reaction terms whose velocities are given by Darcy`s type laws. Such equations govern the water phase, the viable tumor cell phase, the dead tumor cell phase and the host tissue phase. The simplest version reduces to a single equation for the volume fraction of the tumor cells with an advective velocity field depending on the pressure gradient and on the Korteweg force (i.e. the divergence of a suitable adhesion flux). This model is also known as Cahn-Hilliard-Hele-Shaw system. We present an overview of some recent theoretical results on such a system. |
|