题目：Transition-layer solutions in mass-conserving reaction-diffusion

systems for modeling phase separation and pattern formation

时间：2025年12月19日上午10:00-12:00

地点：兴庆校区数学楼2-3会议室

报告人：何小清教授（华东师范大学）

摘要: We develop a rigorous existence theory for radially symmetric stationary solutions with internal transition layers in mass-conserving reaction-diffusion(MCRD) systems---a class of models widely used to describe phase separation and pattern formation in cell polarization, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis suggest that these models can support stationary patterns with sharp internal interfaces, but a rigorous mathematical justification for such transition-layer patterns is still lacking. The central analytical challenge arises from the complex interplay between the global mass-conservation constraint and the singular-perturbation structure of the MCRD system. We overcome these difficulties by combining refined multiscale expansions and spectral analysis in a framework that explicitly incorporates the global mass-constraint. To our knowledge, this work provides the first rigorous construction of transition-layer patterns in MCRD systems and thereby offers a solid theoretical basis for their use in modeling phase separation and pattern formation in biological and ecological systems.

简介：何小清，华东师范大学教授、博士生导师，国家级青年人才计划入选者。2007年在西安交通大学获得学士学位，2013年在明尼苏达大学获得博士学位。2013年至2015年在台湾理论科学研究中心做博士后。她是偏微分方程、应用数学和生物数学等研究领域的青年专家，主要研究兴趣是源自于生物学、物理学和生态学中的非线性椭圆型和抛物型偏微分方程/方程组解的性质及其应用。在 CPAM、JEMS、JDE、CVPDE、JMB 等国际数学期刊发表多篇学术论文。