报告题目：Asymptotic Behavior of Solutions for the Chipot-Weissler Equation with Free Boundary

主 讲 人：张正策

单 位：西安交通大学

时 间：1月12日15:00

腾 讯 ID:715 246 334

摘要：

In this talk, we consider the free boundary problem for the Chipot-Weissler equation. It is well known that global existence or blowup of solutions of nonlinear parabolic equations depends on which one dominating the model, the source or absorption, and on the absorption coefficient for the balance case of them. The aim of the paper is to study the influence of exponents of source and absorption, initial data and free boundary on the asymptotic behavior of solutions. At first, the ecological meaning of this model is explained by deriving the equation and the free boundary condition. Then, local existence and uniqueness are discussed, and the continuous dependence on initial data and comparison principle are proved. Furthermore, the finite time blowup and global solution are given by constructing sub- and super-solutions. In the different ranges of exponents and initial conditions, finite time blowup solutions, global fast solutions and global slow solutions were classified. Finally, the problem with double free boundaries was also discussed.

简介:

张正策，西安交通大学数学与统计学院教授，博士生导师，从事非线性偏微分方程理论及其应用研究，主要对非线性抛物方程的梯度爆破和自由边值问题开展定性研究。主持多项国家自然科学基金项目，教育部基金项目，在国际学术刊物JDE, DCDS, NA, NARWA, JMAA等，发表论文40余篇，多次应邀参加11th AIMS(2016), AMS Spring Section(2011)等国际学术会议并作报告，担任美国数学会评论员。