报告题目：Initial Boundary value problem for some class of wave equations with nonlocal terms
报 告 人：张宏伟 教授
工作单位：河南工业大学
报告时间：2023-5-28（周日） 8:00-10:00
报告地点： 数信学院 3401
报告人简介：张宏伟，博士，河南工业大学二级教授，研究生导师。河南省学科技术带头人，河南省优秀教师，河南省数学学会常务理事、河南省数学教学指导委员会会员、河南省数字图形图像学会常务理事。主要研究方向为非线性偏微分方程、应用泛函分析，先后主持或参加国家自然科学基金以及省、厅级项目28项。在国内外刊物发表学术论文100余篇，其中SCI、EI收录40余篇，出版著作、教材4部，获得科研成果、教学成果奖励10余项。
报告摘要： In this talk, we study the well-posedness, asymptotic stability and blow-upof solution to the initial boundary value problem for some class of nonlinear wave equations with nonlocal terms.
报告题目：Lifespan of smooth solutions to hyperbolic geometric flow equation and rotational compressible Euler equations
报 告 人：王玉柱 教授
工作单位：华北水利水电大学
报告时间：2023-5-28（周日） 10:00-12:00
报告地点： 数信学院3401
报告人简介：王玉柱，教授、博士生导师、河南省高层次人才、华北水利水电大学“大禹学者”特聘教授。在Comm. Partial Differential Equation、J. Differential Equations 等期刊上发表论文50余篇。主持国家自然科学基金项目面上项目和青年项目各1项、主持河南省科技创新杰出青年项目、河南省高校科技创新人才支持计划及河南省高校重点科研项目基础研究专项各1项。主持、参与获省部级科学技术奖励4项。
报告摘要 In this topic, lifespan of smooth solutions to two dimensional hyperbolic geometric flow equation and rotational compressible Euler equations are investigated. The two dimensional hyperbolic geometric flow equation is derived from hyperbolic geometric flow for Riemannian metric. We find that some of quadratic nonlinear terms satisfies the null condition by rearranging the equation. Based on the ghost weight and standard energy estimate, the estimate of solutions and the bootstrap argument, life-span of smooth solutions to two dimensional hyperbolic geometric flow equation is established under the assumption of small data. For the two dimensional rotational compressible Euler equations with nonzero relatively vorticity, by combining the ghost weight energy estimate, global smooth solutions to the two dimensional rotational compressible Euler equations with zero relatively vorticity and the bootstrapping argument, lifespan of smooth solutions is obtained. The result clarifies the influence of nonzero relatively vorticity on lifespan of smooth solutions to two dimensional rotational compressible Euler equations.
报告题目：Convergence problem of Schrödinger equation in Fourier-Lebesgue spaces with rough data and random data
报 告 人：闫 威 教授
工作单位：河南师范大学
报告时间：2023-5-27（六） 16:00-18:00
报告地点： 数信学院 3401
报告人简介：闫威，博士，河南师范大学教授，博士生导师，主要从事调和分析及其应用和初值随机化等方面的研究，曾先后主持国家自然科学基金三项和国家留学基金委项目，以第一作者在. Ann. Inst. H. Poincaré C Anal. Non Linéaire，Indiana Univ. Math. J. Adv. Differential Equations，Differential Integral Equations, J. Differential Equations，Proc. Amer. Math. Soc., Discrete Contin. Dyn. Syst.，Sci. China Math.等发表文章40余篇。
报告摘要In this paper, we consider the convergence problem of Schr\"odinger equation. Firstly, we show the almost everywhere pointwise convergence of Schr\"odinger equation in Fourier-Lebesgue spaces with rough data. Secondly, we show that the maximal function estimate related to one dimensional Schr\"odinger equation can fail with data in $\hat{H}^{s,\frac{p}{2}}(\R)(s<\frac{1}{p})$. Finally, we show the stochastic continuity of Schr\"odinger equation with random data in $\hat{L}^{r}(\R^{n})(2\leq r<\infty)$ almost surely.
