讲座主题：Some recent results on the doubly nonlinear parabolic equations

专家姓名：张超

工作单位：哈尔滨工业大学

讲座时间：2025年05月31日 10:00-11:00

讲座地点：烟台大学承先图书馆报告厅

主办单位：烟台大学数学与信息科学学院

内容摘要：

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.

主讲人介绍：

张超，哈尔滨工业大学数学学院和数学研究院教授、博士生导师. 研究领域为非线性椭圆和抛物型偏微分方程的基础理论，在Math. Ann., JLMS, JFA, Israel J. Math.等权威期刊发表论文60余篇，主持国家自然科学基金项目4项. 目前担任黑龙江省数学会秘书长，国际SCI期刊《Bulletin of Mathematical Sciences》和《Advances in Nonlinear Analysis》编委。