报告题目1：Generalized traveling fronts for  time heterogeneous reaction-diffusion equations in a cylinder

报告人：包雄雄教授，长安大学

报告时间：2025年3月31日（周一）8:30-12:00

报告地点：20-200

报告摘要：In this talk, we are devoted to the study of generalized traveling fronts of time heterogeneous reaction-diffusion equations in a cylinder. Here the reaction term is of Fisher-KPP type and depends in a general way on  . We first investigate the existence and non-existence of generalized traveling wave solutions for such equations. Then we prove some spreading properties for the solution of the corresponding Cauchy problem with compactly supported initial values. We also show the stability of generalized traveling wave solutions by proper modifications of the squeezing technique.

报告人简介：包雄雄，现为长安大学理学院数学与应用数学系教授，从事微分方程、动力系统及其应用研究，主要研究兴趣为非齐次环境下反应扩散方程、非局部扩散方程及系统的行波解与传播速度。自2016年7月博士研究生毕业起在长安大学理学院工作至今。2020年破格晋升教授职称。主持完成国家自然科学基金青年基金1项，陕西省自然科学基金2项。目前主持国家自然科学基金面上项目1项，陕西省数理基础项目1项。获得甘肃省自然科学奖二等奖一项(第三完成人)，主持完成陕西省高等学校科学技术研究优秀成果二等奖。 在JDE, JDDE, JMAA, PAMS, CPAA, ZAMP, DCDS-B等学术期刊上发表论文30余篇。

报告题目2：Elliptic and Parabolic problems involving the Logarithmic Laplacian

报告人：陈虎元教授，江西师范大学

报告时间：2025年3月31日（周一）8:30-12:00

报告地点：20-200

报告摘要：In this talk, we study the logarithmic Laplacian operator, which is a singular integral operator with symbol $2\log |\zeta|$. We show that this operator has the integral representation.  This operator arises as formal derivative   of fractional Laplacians at the origin. We develop the functional analytic framework for Dirichlet problems involving the logarithmic Laplacian on bounded domains and use it to characterize the asymptotics of Dirichlet eigenvalues and eigenfunctions, heat kernel and the Cauchy problem.

报告人简介：陈虎元，江西师范大学教授，法国图尔大学，智利大学，双博士学位，德国洪堡学者。主要从事非线性分析和偏微分方程的研究。先后到德国法兰克福大学、法国巴黎十三大、智利圣母玛利亚大学、日本、塞内加尔等地进行学术访问。在 J. Math. Pures Appl.、 Trans. Amer. Math. Soc.（2篇）、Ann. Inst. H. Poincare-AN（2篇）、J. Funct. Anal.（4篇）、Comm. Part. Diff. Eq.、SIAM J. Math. Anal.、J. Diff. Eq.（5篇）、J. D'Anal. Math.、J. London Math. Soc.等杂志上发表SCI论文60余篇。先后主持国家自然科学基金4项（分别为面上项目、地区项目、天元访问学者项目、青年项目），江西省自然科学基金等多个项目。2021年获江西省自然科学奖二等奖。

报告题目3：Influence of Road-field Diffusion on the Invasion and Competition of Aedes Albopictus and Aedes Aegypti Mosquitoes

报告人：田灿荣教授，盐城工学院

报告时间：2025年3月31日（周一）8:30-12:00

报告地点：20-200

报告摘要：Based on the invasion of Aedes albopictus mosquito along roads and its competition with local Ae. aegypti mosquito in Florida, we propose a two-species competition model with road-field diffusion in which the invasive population not only disperses in the interior of the spatial domain but also moves faster on the boundary of the domain. In the case of strong-weak competition where the invasive species is stronger than the local one, it is shown that solutions converge uniformly to a semi-positive equilibrium such that the invasive species drives the local species out of its habitat. In the case of weak weak competition, solutions converge uniformly to a positive equilibrium such that both species coexist. Numerical simulations are presented to explain the current estimated distributions of these two mosquito species in Florida.

报告人简介：田灿荣，盐城工学院教授，江苏省“333”人才工程第三层次人才项目获得者，研究领域是生物数学，主要研究成果发表在SIAM J on Applied Mathematics, SIAM J on Applied Dynamical systems, Journal of Differential Equations, Journal of Computational Physics, Journal of Mathematical Biology等期刊，主持国家自然科学基金3项，江苏省自然科学基金1项。

报告题目4：Propagation phenomena for diffusive SIS epidemic models

报告人：张亮教授，兰州大学

报告时间：2025年3月31日（周一）8:30-12:00

报告地点：20-200

报告摘要：This talk is concerned with the propagation phenomena for a class of susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with two different kinds of incidence posed on unbounded domain. The first goal of this work is to show how the localized initial introductions of infective behave spatially and then the asymptotic speed of spread for the infection is derived to the model with separable incidence (e.g., mass-action mechnism) based on the weak dissipativity and uniform persistence idea on dynamical system.   In the case where the standard incidence is taken into consideration, the existence of the asymptotic speed of spread and the full information on the traveling wave solutions are presented.

报告人简介：张亮，兰州大学数学与统计学院青年教授。2016年毕业于兰州大学，获理学博士学位，并留校任教。主要从事反应扩散方程、应用动力系统相关研究。目前已在Trans. Amer. Math. Soc., J. Differential Equations, J. Dyn. Differ. Equ., J. Evol. Equ., Euro. J. Appl. Math.等学术期刊发表学术论文30余篇。2019年获甘肃省自然科学二等奖，主持完成国家自然科学基金青年基金项目1项，中央高校基本科研业务费2项，目前主持国家自然科学基金面上项目1项。

报告题目5：Entire Solutions to a advective Fisher-KPP Equation on the half line

报告人：锁晋喆博士，安徽师范大学

报告时间：2025年3月31日（周一）8:30-12:00

报告地点：20-200

报告摘要：Entire solutions to reaction-diffusion equations are those whose time is defined on the whole real number line. Together with equilibrium solutions and traveling wave solutions, they can help people understand the global dynamic behavior of the equations. In recent decades, many scholars have constructed some entire solutions for various reaction-diffusion equations and obtained abundant results. In this talk, several kinds of reaction-diffusion equations are considered and some new entire solutions are constructed for them. Here, we give some new entire solutions to (continuous and discrete) reaction-diffusion equation on the real semi-axis, and describes the  - limit set, which improves the type of entire solutions of the reaction-diffusion equation.

报告人简介：锁晋喆，安徽师范大学数学与统计学院讲师，主要从事反应扩散方程整解的研究，研究成果发表在J. Differential Equations、Nonlinear Anal.等期刊上。

报告题目6：Isolated singularity for semilinear elliptic equations

报告人：陈虎元教授，江西师范大学

报告时间：2025年3月31日（周一）14:00-15:00

报告地点：20-308

报告摘要：In this talk, I will introduce the singular solutions of semilinear elliptic equations with source and absorption nonlinearities in thesetting fractional Laplacian. We will show the role of nonlocal property in the analysis of isolated singularities.

报告人简介：陈虎元，江西师范大学教授，法国图尔大学，智利大学，双博士学位，德国洪堡学者。主要从事非线性分析和偏微分方程的研究。先后到德国法兰克福大学、法国巴黎十三大、智利圣母玛利亚大学、日本、塞内加尔等地进行学术访问。在 J. Math. Pures Appl.、 Trans. Amer. Math. Soc.（2篇）、Ann. Inst. H. Poincare-AN（2篇）、J. Funct. Anal.（4篇）、Comm. Part. Diff. Eq.、SIAM J. Math. Anal.、J. Diff. Eq.（5篇）、J. D'Anal. Math.、J. London Math. Soc.等杂志上发表SCI论文60余篇。先后主持国家自然科学基金4项（分别为面上项目、地区项目、天元访问学者项目、青年项目），江西省自然科学基金等多个项目。2021年获江西省自然科学奖二等奖。

邀请人：非线性分析与PDE团队