题目：Global well-posedness of coupled parabolic systems for two-component combustion 

时间：2024年4月19日（周五）8:00-10:00

地点：数学与统计楼213会议室

报告人：徐润章 教授 哈尔滨工程大学

摘要：

The initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in order to classify the initial data for the global existence, finite time blowup and longtime decay of the solution for two-component combustion. The whole study is conducted by considering three cases according to initial energy: low initial energy case, critical initial energy case and high initial energy case. For the low initial energy case and critical initial energy case the sufficient initial conditions of global existence, long time decay and finite time blowup are given to show a sharp-like condition. And for the high initial energy case the possibility of both global existence and finite time blowup is proved first, and then some sufficient initial conditions of finite time blowup and global existence are obtained respectively.

报告人简介：

徐润章，哈尔滨工程大学数学科学学院教授，博士生导师，黑龙江省数学会常务理事，黑龙江省青年学术骨干。近二十年来致力于利用位势井理论研究非线性偏微分方程的解关于初值的依赖问题，并针对偏微分方程中的三大基本模型方程(波方程，热方程和薛定谔方程)的适定性理论，将碎片化研究提升到同一框架下的系统化研究，开创了全能级系统化研究初值与解的适定性关系的新范式。在非线性偏微分方程的解关于初值的依赖问题的研究方向，至今已发表SCI论文110多篇，包括Archive for Rational Mechanics and Analysis, Journal of Functional Analysis， SIAM Journal on Mathematical Analysis，Science China Mathematics等国内外著名数学期刊，被引总频次1500余次，单篇超40次引用的论文9篇，热点论文(数学Top 0.1%) 1篇，ESI高被引论文(数学Top 1%) 7篇。