| Abstract | We study a free boundary problem that naturally arises in a 2-D tumor growth model with nutrient. In this model, the tumor cells proliferate by consuming the nutrient locally, and meanwhile they migrate into ambient empty space because of an incompressibility constraint on the cell density. We shall focus on evolution of the tumor boundary, which couples strongly with the dynamics of nutrient in the bulk. We will show, under suitable assumptions, global well-posedness of evolution of the tumor boundary, provided that it is initially close to a circle. We will also establish its long-time convergence to a circular shape as well as a (sharp) decay estimate. Discussions will be made on several related problems. |
