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     **15年“理学之美”名师论坛 第10讲

     报告题目：Free Boundary Problems in Mathematical Biology
     时 间：**15年5月22日下午3:00-4:00
     地 点：建龙报告厅
     报告内容简介：
     In a free boundary problem one seeks to solve a system of PDEs in a domain which is not known in advance; determining the domain is a part of the problem. A classical example is the Stefan problem of melting of ice: the temperature satisfies the heat equation in the water region, and this region is changing as the ice melts. Other examples include contact problems in mechanics, jets and cavities in fluid, water waves and the Hele-Shaw model.

     In this talk, I will describe more recent free boundary problems which arise in biology. The first one is a system of PDEs modeling the growth of a tumor, and I will discuss the analysis of symmetry breaking bifurcations from a spherical tumor, which may be viewed as the initiation of metastasis. The second model is a chronic wound which is contracting as the wound heals. The third example is the development of a plaque in the artery, a disease called atherosclerosis, which is the leading cause of death worldwide. In all these models, I will state some mathematical results and suggest challenging open problems.

     报告人简介：
Avner Friedman，美国俄亥俄州立大学数学特聘教授，美国科学院院士，美国艺术与科学院院士，国际著名数学家，在偏微分方程、随机PDE、自由边界问题、控制论和数学生物学等领域取得了杰出成就。曾任美国工业与应用数学学会主席，明尼苏达大学工业数学与应用研究所所长，美国数学生命科学研究所所长，近** 个国际著名数学杂志编委。出版著作**余部，发表研究论文500余篇，其中绝大多数著作和论文被美国数学会数学评论网超高次数引用.