講座主題：Some recent results on the doubly nonlinear parabolic equations
專家姓名：張超
工作單位：哈爾濱工業大學
講座時間：2025年05月31日 10:00-11:00
講座地點：煙臺大學承先圖書館報告廳
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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，哈爾濱工業大學數學學院和數學研究院教授、博士生導師. 研究領域為非線性橢圓和拋物型偏微分方程的基礎理論，在Math. Ann., JLMS, JFA, Israel J. Math.等權威期刊發表論文60余篇，主持國家自然科學基金項目4項. 目前擔任黑龍江省數學會秘書長，國際SCI期刊《Bulletin of Mathematical Sciences》和《Advances in Nonlinear Analysis》編委。
