广州大学数学大讲坛第六期

第五十九讲——哈尔滨工程大学徐润章教授学术报告

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

时间：2022年9月29日（周四）下午2：30-3：30

地点：腾讯会议（会议ID:810-286-255）

报告人：徐润章教授

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：

徐润章教授，博士生导师，“龙江学者”青年学者，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波方程，热方程和薛定谔方程的解关于初值的依赖问题，将碎片化研究提升到系统化研究，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，已取得一系列国际领先的重要成果。至今已在“Archive for Rational Mechanics and Analysis”、“Journal of Functional Analysis”、“SIAM Journal on Mathematical Analysis”、“Journal of Differential Equations”、“Zeitschrift fur angewandte Mathematik und Physik”、“Physica D”、“Advances in Nonlinear Analysis”等期刊发表SCI论文110余篇，被引总频次1368次。同时现任国际期刊“Advances in Nonlinear Analysis”主编、Applied Numerical Mathematics编委、Boundary Value Problems副主编、Electronic Research Archive编委、Opuscula Mathematica编委、“中国工业与应用数学会简讯”编委等学术职务。