题 目：The critical initial condition to Thin-film equations and the best constant of Nagy’s functional inequalities
报告人：王金环 教授 （辽宁大学数学院）
地 点： 西大楼108室
时 间： 2018年11月27日（星期二）上午10:00-11:00
摘 要: In many physical and biological systems, there are some competing effects such as focus and de-focus, attraction and repulsion, spread and concentration. These competing effects usually are represented by terms with different signs in a free energy. The dynamics of the physical system sometimes can be de- scribed by a gradient flow driven by the free energy. Some functional inequalities can be used to determine the domination among these competing effects in the free energy, and provided critical initial conditions to distinguish global existence and blow-up of solutions to the models. For example, the Hardy-Littlewood-Sobolev inequality vs parabolic-elliptic Keller-Segel model, the Nirenberg-Gagliardo (N-G) inequality vs nonlinear Schroedinger equation and the Sobolev inequality vs degenerate parabolic-parabolic Keller-Segel model etc.
In this talk, we will show the relationship between Nagy’s inequalities and the critical initial conditions to some thin film equations. In particular, we will prove the existence of weak solutions to an one-dimensional thin-film equation if the initial mass is less than the critical initial condition, which is from the one-dimensional Nagy’s inequality. Moreover, we derive the best constant of a higher dimensional Nagy’s inequality to determine the initial criteria for the higher dimensional thin-film equation.