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报告题目： Global existence and blow up of solutions for pseudo-parabolic equation with singular potential

报告人：徐润章教授

报告时间：2023年11月20日下午14：30

腾讯会议：635-360-903

邀请人：廖梦兰

报告摘要：In this talk, we like to report a study in the initial boundary value problem of pseudo-parabolic equation with singular potential, in order to classify the initial data for the global existence, finite time blowup and longtime decay of the solution. 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. Also two different strategies are applied to estimate the upper bounds of the blowup time for the negative initial energy blowup and positive initial energy blowup respectively.  And for the high initial energy case, the finite time blowup is proved.

报告人简介：哈尔滨工程大学数学科学学院教授，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。至今已发表SCI论文110余篇，包括ARMA, JFA, CVPDE, JDE, SIMA, ZAMP, Physica D, ANA, QAM, DCDS, ACV, JGA, JMP, 中国科学数学，数学学报等。《哈尔滨工程大学学报》编委， Advances in Nonlinear Analysis 主编， Communications in Analysis and Mechanics主编，Applied Numerical Mathematics编委， Boundary Value Problems 副主编; Electronic Research Archive (ERA)编委；The Annals of the University of Craiova - Mathematics and Computer Science series 编委，Opuscula Mathematica编委，《中国工业与应用数学会简讯》编委。