报告题目1：Propagation phenomena of reaction-diffusion equations with effective boundary condition in a strip

报告人：何俊锋副教授，深圳技术大学

报告时间：2026年6月6日（周六）14:30-17:30

报告地点：20-200

报告摘要：In this talk, we mainly concerned with propagation phenomena of reaction-diffusion equations with effective boundary condition in a strip, which is meant to model the physical scenario of a road with fast diffusion as the width of the road shrinks. We show that, in an infinite strip, with effective boundary condition on one boundary and homogeneous Neumann boundary condition on the other, the reaction-diffusion equation for the three classical nonlinear terms admits traveling wave solutions. Precise decay rates of the traveling wave solutions are also derived.

报告人简介：何俊锋，深圳技术大学人工智能学院副教授，深圳市后备级高层次人才。博士毕业于首都师范大学应用数学专业。武汉大学－南方科技大学联合培养博士后。近年来，主持国家自然科学基金青年基金、中国博士后面上项目以及深圳市博士后出站科研项目各一项；科研项目主要聚焦于反应扩散方程的传播现象，累计发表SCI学术论文10余篇，研究成果主要发表在ARMA、JDE、NA及ZAMP等国外著名SCI期刊上。

报告题目2：Global dynamics of a two-species Lotka-Volterra competition-diffusion-advection system with general carrying capacities and intrinsic growth rates

报告人：唐德副教授，中山大学

报告时间：2026年6月6日（周六）14:30-17:30

报告地点：20-200

报告摘要：We study a Lotka-Volterra competition-diffusion-advection system with general intrinsic growth rates and carrying capacities for two competing species in heterogeneous closed environments, where individuals are exposed to unidirectional flow (advection) but no individuals pass through the boundary. Firstly, we establish the classification of linear stability for the two semi-trivial steady states. Then, we rule out the existence of co-existence steady state under some special conditions, which seems non-trivial. Combining these two aspects with the theory of monotone dynamical systems, we prove the main results. Our results suggest that the spatial distributions of carrying capacities and intrinsic growth rates totally change the “evolutionary stability strategy of species”. Precisely, if the carrying capacities increase fast, then “slower diffuser always prevails”; if the carrying capacities increase slow, then “faster diffuser always prevails”; if the carrying capacities increase intermediately, then two species coexist.

报告人简介：唐德，中山大学数学学院（珠海），副教授，硕士生导师。主要研究领域为微分方程、动力系统和生物数学，研究成果发表在SIMA，JDE，Nonlinearity，SIADS，JDDE，JMB，Phys.D，DCDS等国际重要期刊上。主持（完成）1项国家自然科学基金青年项目、2项广东省自然科学基金面上项目等。

报告题目3：Localized patterns and their dynamics in a diffusive population-toxicant model with negative toxicant-taxi

报告人：谢双全副教授，湖南大学

报告时间：2026年6月6日（周六）14:30-17:30

报告地点：20-200

报告摘要：We investigate a population-toxicant model with negative toxicant-taxis that exhibits rich spatiotemporal spike dynamics. In the limit of large toxicant-taxis sensitivity, we construct asymptotic equilibrium spike solutions using the matched asymptotic expansions. We prove that boundary spike solutions are linearly stable at the leading order. In contrast, by deriving an explicit asymptotic formula for the translational eigenvalue, we show that interior spike solutions are inherently unstable to translations of the spike profile. We further derive a reduced ordinary differential equation governing the fast motion of the spike center and slow motion of the spike height in environments with spatially homogenous and inhomogeneous toxicant inputs. Our results reveal that spikes drift rapidly toward the nearest domain boundary in homogeneous environments, while in strongly inhomogeneous environments, they converge to locations of minimal toxicant concentration.

报告人简介：谢双全，湖南大学数学学院副教授。武汉大学本硕，加拿大戴尔豪斯大学应用数学博士，曾任日本东北大学助理教授。主要从事与生物数学相关的建模和理论分析工作。在JDE, Nonlinearity, SIADS, Physica D, JNS等杂志上发表论文十余篇。

邀请人：无穷维动力系统和偏微分方程研究所