报告人：沈建和（福建师范大学）

邀请人：李骥

报告时间：2024年5月10日（星期五）10:30-12:00

报告地点：科技楼南楼706室

报告题目：Algebraically Decaying Pulses in a Degenerated Gierer-Meinhardt Equation with a Higher-order Nonlinearity

报告摘要：This paper studies the existence and stability of algebraically delaying pulses in Gierer-Meinhardt equation with slowly degenerated nonlinearity by developing geometric singular perturbation theory (GSPT) and NonLocal Eigenvalue Problem (NLEP) method. Firstly, by utilizing that the critical manifold is non only normally hyperbolic but also invariant, we rigorously prove the existence of algebraically delaying pulses by combining GSPT with Melnikov method. It is found that this model admits a unique algebraically delaying pulse. However, the slowly degenerated nonlinearity results in that the linearized matrix associated with the eigenvalue problem no longer approaches to the constant matrix exponentially. So we must solve the resulting linear “time-varying” problem. By classifying the powers of the slowly degenerated nonlinearity, we introduce different special functions including Whittaker function and Bessel function to solve the linear “time-varying” problem explicitly. Thus the spectral (in)stability criteria on the algebraically delaying pulse is set up by matching the slow and fast segments of the localized eigenfunctions. Several examples are performed to verify the theoretical framework.

报告人简介：沈建和，福建师范大学数学与计算机科学学院教授，博士生导师，副院长。中国数学会奇异摄动专业委员会副主任委员。入选百千万人才工程省级人选（2019年）、福建省高校新世纪优秀人才支持计划（2017年）、福建省高校杰出青年科研人才培育计划（2015年）。