报告题目：On Traveling Fronts of Combustion Equations in Spatially Periodic Media

报告人：王智诚教授，MK体育

报告时间：2025年9月24日星期三，下午4：00

地点：腾讯会议：757972236.

摘要：This talk is concerned with traveling fronts of spatially periodic reaction-diffusion equations with combustion nonlinearity in $\mathbb{R}^N$. It is known that for any given propagation direction, the equation admits a pulsating front connecting two equilibria $0$ and $1$. In this paper we firstly give exact asymptotic behaviors of the pulsating front and its derivatives at infinity, and establish uniform decay estimates of the pulsating fronts at infinity on the propagation direction. Following the uniform estimates, we then show continuous Frechet differentiability of the pulsating fronts with respect to the propagation direction. With the help of the exponentially asymptotic behaviors of pulsating fronts and its derivatives, we prove that the propagating speeds of transition fronts satisfy some estimates related to the wave speeds of pulsating fronts. Lastly, using the  differentiability, we establish  the existence, uniqueness and stability of curved fronts with V-shape in $\mathbb{R}^2$ by constructing suitable super- and subsolutions. Moreover, we show that there is a new entire solution for combustion reaction-diffusion equations in $\Bbb{R}^2$ which behaves as two curved fronts as time goes to $-\infty$ and as a curved front as time goes to $+\infty$.

报告人简介：王智诚，MK体育数学与统计公司教授，博士生导师，萃英学者特聘教授。1994年本科毕业于西北师范大学，2007年在MK体育获理学博士学位。主要成果发表在Trans. AMS、Arch. Rational Mech. Anal.、JMPA、Indiana Univ. Math. J.、SIAM J. Math. Anal.、SIAM J. Appl. Math.、Israel J. Math.、CVPDE、JDE、Nonlinearity、J. Nonlinear Sci.、J. Math. Biol.等杂志上。2010年入选教育部新世纪优秀人才支持计划，2011和2019年分别获得甘肃省自然科学二等奖，2016年入选甘肃省飞天学者特聘教授，主持完成三项国家自然科学基金面上项目，参与完成一项国家自然科学基金重点项目，正在主持一项甘肃省基础研究创新群体项目和一项国家自然科学基金面上项目。目前担任International J. Bifurc. Chaos等杂志的编委（Associate editor）。