TUMOR INVASION MODEL WITH A RANDOM MOTILITY OF TUMOR CELLS DEPENDING UPON EXTRACELLULAR MATRIX

摘要

We treat with a tumor invasion model of Chaplain-Anderson type with a constraint condition, which was originally proposed in [1]. Especially, we consider the case that a random motility of tumor cells depends upon the extracellular matrix, which is also the unknown function in the tumor invasion model, as well as the space and time variables. Besides, the constraint condition also depends upon the densities of tumor cells and the extracellular matrix. The main objective of this paper is to show the existence of time global solutions to the tumor invasion model with the constraintcondition by using the theory of a quasi-variational inequality established by R. Kano et al. in [8].