報告人：王智誠 (蘭州大學)

報告題目：Periodic traveling waves and propagating terraces for multistable nonlinearity in cylinders

報告摘要：This talk is devoted to the study of a class of reaction-advection-diffusion equations in cylinders, where the nonlinearity is a tristable or multistable nonlinearity. We establish the alternative of wave solutions, that is, either there is a unique, asymptotically stable periodic traveling wave connecting 0 to 1 directly, or there is a unique propagating terrace connecting 0 to 1. Under the assumption that all wave speeds in propagating terrace are not equal to each other, we further obtain that the propagating terrace is asymptotically stable if it exists. Moreover, the sufficient and necessary conditions for the existence of periodic traveling waves connecting 0 to 1 are given respectively. Our arguments are based on the parabolic maximum principle, sliding method and the super- and sub-solution method.

報告時間：2024年12月7日（星期l六）8:30-10:00

報告地點：科技樓706會議室

邀請人：李骥

報告人簡介：王智誠，蘭州大學88858cc永利教授，博士生導師，萃英學者特聘教授。1994年本科畢業于西北師範大學，2007年在蘭州大學獲理學博士學位。主要成果發表在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.等雜志上。2010年入選教育部新世紀優秀人才支持計劃，2011和2019年分别獲得甘肅省自然科學二等獎，2016年入選甘肅省飛天學者特聘教授，主持完成三項國家自然科學基金面上項目，參與完成一項國家自然科學基金重點項目，正在主持一項甘肅省基礎研究創新群體項目和一項國家自然科學基金面上項目。目前擔任兩個SCI雜志International  J.  Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的編委（Associate editor）。