为了提高团队的科研水平，促进学术交流，微分方程理论及其应用科研团队定于2023年4月21日（星期五）下午14：30-17:00在基础实验实训中心413室举行学术交流会。

本次交流会主要有以下2个方面：

1．学术报告

2. 团队成员近期研究进展及团队发展交流。

欢迎大家参加交流。

学术报告1

报告人：李磊

报告题目：Dynamics for nonlocal diffusion problems with free boundary

摘要：We consider two nonlocal diffusion problems with a free boundary, and prove that their longtime behaviors are governed by spreading-vanishing dichotomy. When spreading happens, their spreading speeds and asymptotic behaviors are obtained; accelerated spreading will occur if and only if a threshold condition is violated by kernel function. Moreover, the rate of accelerated spreading is discussed for some algebraic decay kernels. This topic is based on the joint works with Prof. Wantong Li, Prof. Mingxin Wang and Dr. Xueping Li.

报告人简介：李磊，博士，2021年博士毕业于哈尔滨工业大学。主要研究反应扩散方程（组）的长时间行为，在JDE, JDDE, SCM, ZAMP, PRSEA等杂志发表论文10余篇。

学术报告2

报告人：卫丹

报告题目：具空间结构和异质性的反应扩散模型动力学研究

摘要：Reaction-diffusion models play a crucial role in the development of epidemiology and biological population dynamics. With the deepening of research, scholars have found that the migration of species and the spread of microorganisms in space may not only be random diffusion, but also directional movement due to external environmental forces such as water currents, ocean currents, quicksand and wind direction. In addition, species and microorganisms may also have a certain ability to discriminate some external signals, such as spouse, food, smells or some chemicals, and thus produce chemotactic movement. For this reason, researchers add advection term or chemotaxis term to the classical reaction-diffusion equation to improve the practical significance of the mathematical model. In this work, the local and global dynamics of the reaction-diffusion model with different spatial structures (i.e., spatial heterogeneity, time delay effect, advection effect and chemotaxis effect) are investigated by using the implicit function theorem, Lyapunov-Schmidt reduction method, central manifold theorem, normal form theory, local bifurcation theory, Banach's fixed point theorem, parabolic regularity theory, a priori estimation, Moser iteration, Lyapunov functional method and LaSalle's invariance principle.

报告人简介：卫丹，博士，2022年毕业于湖南大学数学学院，师从郭上江教授。主要从事“微分方程与动力系统”的相关研究工作，在NA-TMA，DCDS-B等国际期刊发表SCI论文4篇。