講座主題：Some recent results on the doubly nonlinear parabolic equations
專家姓名：張超
工作單位：哈爾濱工業(yè)大學(xué)
講座時(shí)間：2025年05月31日 10:00-11:00
講座地點(diǎn)：煙臺(tái)大學(xué)承先圖書館報(bào)告廳
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
Doubly nonlinear parabolic equations arise in numerous applications of physics.Despitetheirimportance, acomplete mathematical understanding of these equations is yet to be established. In this talk, we present a new type of weak Harnack estimates for the weak supersolutions to a doubly nonlinear nonlocal p-Laplace equation, which is modeled on the nonlocal Trudinger equation. In addition, we give a Harnack inequality of nonnegative weak solutions to the doubly nonlinear mixed local and nonlocal parabolic equations. Our proof is based on the expansion of positivity together with a comparison argument. The challenges consist in controlling subtle interaction between the nonlocal feature and the space-time growth exponents.
主講人介紹：
張超，哈爾濱工業(yè)大學(xué)數(shù)學(xué)學(xué)院和數(shù)學(xué)研究院教授、博士生導(dǎo)師. 研究領(lǐng)域?yàn)榉蔷€性橢圓和拋物型偏微分方程的基礎(chǔ)理論，在Math. Ann., JLMS, JFA, Israel J. Math.等權(quán)威期刊發(fā)表論文60余篇，主持國(guó)家自然科學(xué)基金項(xiàng)目4項(xiàng). 目前擔(dān)任黑龍江省數(shù)學(xué)會(huì)秘書長(zhǎng)，國(guó)際SCI期刊《Bulletin of Mathematical Sciences》和《Advances in Nonlinear Analysis》編委。
