報告題目： Global existence and blow up of solutions for pseudo-parabolic equation with singular potential

報告人：徐潤章教授

報告時間：2023年11月20日下午14：30

騰訊會議：635-360-903

邀請人：廖夢蘭

報告摘要：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.

報告人簡介：哈爾濱工程大學數學科學學院教授，博士生導師，“龍江學者”青年學者，黑龍江省數學會常務理事，黑龍江省青年學術骨幹。近二十年來緻力于利用位勢井理論研究非線性偏微分方程的解關于初值的依賴問題，并針對偏微分方程中的三大基本模型方程(波方程，熱方程和薛定谔方程)的适定性理論，将碎片化研究提升到同一框架下的系統化研究，開創了全能級系統化研究初值與解的适定性關系的新範式。至今已發表SCI論文110餘篇，包括ARMA, JFA, CVPDE, JDE, SIMA, ZAMP, Physica D, ANA, QAM, DCDS, ACV, JGA, JMP, 中國科學數學，數學學報等。《哈爾濱工程大學學報》編委， Advances in Nonlinear Analysis 主編， Communications in Analysis and Mechanics主編，Applied Numerical Mathematics編委， Boundary Value Problems 副主編; Electronic Research Archive (ERA)編委；The Annals of the University of Craiova - Mathematics and Computer Science series 編委，Opuscula Mathematica編委，《中國工業與應用數學會簡訊》編委。