Joint project with physicists to develop a continuous model for tumor growth. In the recent biomechanical theory of cancer growth, solid tumors are considered as liquidlike materials comprising elastic components. In this fluid mechanical view, the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate, with the latter depending on the local cell density (contact inhibition) or/and on the mechanical stress in the tumor. The individual based model (IBM) has already been tested in accordance with experiments. Quantitative matching can be found by comparing the numerical results of the continuous model and IBM. 
For the two by two degenerate parabolic/elliptic reactiondiffusion system model, we prove that there exist traveling waves above a minimal speed,
and analyze their shapes. In particular, the incompressible cells limit is very singular and related to the HeleShaw equation. 
