Speaker: Yuming Paul Zhang (Auburn)

 

Title: Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models

 

 

Abstract: In this talk, I will first provide an overview of my research, followed by an introduction to Porous Medium Equations (PMEs). The focus will then shift to my recent work on the incompressible limit of PMEs. While most literature studies the convergence of solutions in this limit, we establish the first convergence result of free boundaries in the Hausdorff distance. To achieve this, we develop uniform propagation and stability properties of free boundaries. As a further consequence, we derive an upper bound for the Hausdorff dimension of the free boundary and show that the limiting free boundary has finite \((d-1)\)-dimensional Hausdorff measure.

 

 

Host: Le Chen