In this talk, we will discuss an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term that models tumor growth. We first prove the existence of global weak solutions as well as the existence of unique local strong solutions in both 2D and 3D. Then we investigate the qualitative behavior of solutions in details when the spatial dimension is two. More precisely, we prove that the strong solution exists globally and when the mass source term is be asymptotically autonomous, every global solution converges to a single steady state as time goes to infinity.
Biography
Hao Wu is a Professor at School of Mathematical Sciences of Fudan University. His current research interests focus on theoretical investigating nonlinear evolution equations and infinite dimensional nonlinear dynamical systems arising in physics, material science, biology, engineering and other applied areas.