报告人：吴昊

工作单位: 复旦大学

报告时间：2018年11月17日9:00

报告地点：数学与统计学院一楼报告厅

报告摘要：

In this talk, we discuss the Cahn–Hilliard–Hele–Shaw system with a physically relevant potential (i.e., of logarithmic type). This choice ensures that the (relative) concentration difference takes values within the admissible range [-1, 1]. We first prove the existence of a global weak solution with finite energy. Then, in dimension two, we show the uniqueness and regularity of the global weak solution, in particular, we prove that any two-dimensional weak solution satisfies the so-called strict separation property. When the spatial dimension is three, we prove the existence of a unique global strong solution, provided that the initial datum is regular enough and sufficiently close to any local minimizer of the free energy, which also yields the local Lyapunov stability of the local minimizer itself.

报告人简介：

吴昊，2007年获复旦大学理学博士学位，现任复旦大学数学科学学院教授、博士生导师。吴昊主要从事非线性发展方程适定性和大时间渐近性态的研究，在 Arch. Rational Mech. Anal.，SIAM J. Math. Anal.，Math. Models Methods Appl. Sci.，Ann. Inst. H. Poincaré Anal. Non Linéaire，J. Differential Equations 等数学期刊发表论文40余篇。2015年获中国工业与应用数学学会优秀青年学者奖，2016年入选上海市青年拔尖人才。