The Cahn-Hilliard Equation with Dynamic Boundary Conditions


主题:   The Cahn-Hilliard Equation with Dynamic Boundary Conditions主讲人:   吴昊地点:   松江校区2号学院楼331理学院报告厅时间:   2018-05-18 10:30:00组织单位:   非线性科学研究所

主讲人简介:吴昊,复旦大学数学科学学院教授。2003年毕业于复旦大学获理学学士学位,2007年毕业于复旦大学获理学博士学位。主要研究在材料科学与力学中有重要应用的几类非线性发展方程的适定性和稳定性理论,并取得一系列成果。目前,已在《Arch. RationalMech. Anal.》,《SIAM J. Math. Anal.》,《Ann. Inst. H. Poincare Anal. Non Lineaire》,《Math. ModelsMethods Appl. Sci.》,《Calc. Var. Partial Differential Equations》,《J. DifferentialEquations》等高水平杂志上发表论文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。

内容摘要:The Cahn-Hilliard equation is a fundamentalmodel that describes phase separation processes of binary mixtures. In order to account for possible short-range interactions of the material with the solidwall, various dynamic boundary conditions have been proposed in the literature.In this talk, we introduce a new class of dynamic boundary conditions for the Cahn-Hilliard equation. The derivation is based on an energetic variational approach that combines the least action principle and Onsager's principle of maximumenergy dissipation. Then under suitable assumptions, we prove the existence anduniqueness of global weak/strong solutions to the initial boundary problem withor without surface diffusion. Furthermore, we establish the uniqueness of asymptotic limit as time goes to infinity and characterize the stability oflocal energy minimizers for the system.

讲座主持:秦玉明 教授


视频:   摄影: 撰写:秦玉明  信息员:唐晓亮  编辑:朱一超



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