报告人：沈建和（福建师范大学）

邀请人：李骥

报告时间：2021年6月3日（星期四）10:30-12:00

报告地点：腾讯会议 ID：115 103 099

报告题目：The problems of reaction-diffusion systems with strongly localized impurities and singular perturbation

报告摘要：In this talk, we point out that reaction-diffusion systems with strongly localized impurities are singular perturbation problems with slow-fast structures. The strong, spatially localized, nonlinear impurities have great impacts on the existence, stability and bifurcations of localized structures in systems of linear reaction-diffusion equations. By taking advantage of the multiple -scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single - and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-) pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. Also we show that non-monotonic interior layer (non-monotonic heteroclinic orbits) can be generated in nonlinear, scalar reaction-diffusion equation with strong, spatially localized, nonlinear impurities.

报告人简介：沈建和，福建师范大学数学与信息学院教授、博士生导师、数学系副主任，入选福建省高校新世纪优秀人才支持计划，2015年入选福建省高校青年科研人才培育计划；2015年获评福建师范大学优秀青年骨干教师。目前兼任中国数学会奇异摄动专业委员会委员、福建省生物数学学会秘书长。主要从事奇异摄动理论及其应用问题的研究。在《Phil. Trans. Royal Soc. A》，《Phy.D》,《J. Differential Equations》等发表多篇论文。