报告题目：Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models

报告人：童嘉骏（北京大学）

报告时间：2024年4月20日11:10-12:40

报告地点：数统学院208（腾讯会议 932 495 5583）

邀请单位：福州大学数学与统计学院

报告内容简介：

We investigate the general Porous Medium Equations with drift and source terms that model tumor growth. Incompressible limit of such models has been well-studied in the literature, where convergence of the density and pressure variables are established, while it remains unclear whether the free boundaries of the solutions exhibit convergence as well. In this talk, we shall present an affirmative result by showing that the free boundaries converge in the Hausdorff distance in the incompressible limit. It relies on quantifying the relation between the free boundary motion and spatial average of the pressure, and establishing a uniform-in-m strict expansion property of the pressure supports. As a corollary, we derive upper bounds for the Hausdorff dimensions of the free boundaries and show that a good part of the limiting free boundary has finite (d-1)-dimensional Hausdorff measure. This is based on a joint work with Yuming Paul Zhang.

报告人简介：

童嘉骏，北京大学北京国际数学研究中心助理教授，博士毕业于纽约大学库朗数学研究所，曾在美国加州大学洛杉矶分校从事博士后研究。主要研究方向为自由边界问题、流体方程、以及变分问题。目前已在包括《Comm. Pure Appl. Math.》,《Arch. Ration. Mech. Anal.》,《SIAM J. Appl. Math.》,《Comm. Math. Phys.》等国际著名SCI数学期刊上发表论文10余篇。