光華講壇——社會(huì)名流與企業(yè)家論壇第6637期
主題：Global existence and blow up of solutions for pseudo-parabolic equation with singular potential奇異勢(shì)偽拋物方程解的全局存在性與爆破
主講人：哈爾濱工程大學(xué) 徐潤(rùn)章教授
主持人：數(shù)學(xué)學(xué)院 梁之磊教授
時(shí)間：11月3日 17:00-17:40
主辦單位：數(shù)學(xué)學(xué)院 科研處
主講人簡(jiǎn)介：
哈爾濱工程大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博士生導(dǎo)師，“龍江學(xué)者”青年學(xué)者，黑龍江省數(shù)學(xué)會(huì)常務(wù)理事，黑龍江省青年學(xué)術(shù)骨干。Advances in Nonlinear Analysis 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(guó)工業(yè)與應(yīng)用數(shù)學(xué)會(huì)簡(jiǎn)訊》編委。 “中羅應(yīng)用數(shù)學(xué)中心(CRAM)”創(chuàng)始成員，美國(guó)數(shù)學(xué)科學(xué)研究所學(xué)術(shù)期刊科學(xué)顧問(wèn)。
內(nèi)容提要：
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 positve initial energy blowup respectively. And for the high initial energy case, the finite time blowup is proved.
我們想報(bào)告一項(xiàng)關(guān)于具有奇異勢(shì)的偽拋物線(xiàn)方程的初始邊值問(wèn)題的研究，以便對(duì)解的全局存在性、有限時(shí)間爆炸和長(zhǎng)期衰減的初始數(shù)據(jù)進(jìn)行分類(lèi)。 整個(gè)研究根據(jù)初始能量考慮三種情況：低初始能量情況、臨界初始能量情況和高初始能量情況。 對(duì)于低初始能量情況和臨界初始能量情況，給出了全局存在、長(zhǎng)時(shí)間衰減和有限時(shí)間爆破的充分初始條件，以表現(xiàn)出類(lèi)尖銳條件。 還應(yīng)用兩種不同的策略來(lái)分別估計(jì)負(fù)初始能量爆炸和正初始能量爆炸的爆炸時(shí)間的上限。 對(duì)于高初始能量的情況，證明了有限時(shí)間爆破。
