2024西安電子科技大學(xué)

非線性分析、微分方程與動力系統(tǒng)系列報告

報告信息

(以姓氏拼音為序)

On the periodic traveling waves and propagating terraces of multistable reaction-advection-diffusion equations in cylinders

盛偉杰 哈爾濱工業(yè)大學(xué)

摘要：This talk is concernd with the periodic traveling waves and propagating terraces for multistable reaction-advection-diffusion equations in cylinders. 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.

報告人簡介：盛偉杰?，哈爾濱工業(yè)大學(xué)數(shù)學(xué)學(xué)院教授、博士生導(dǎo)師。2013年畢業(yè)于蘭州大學(xué)并獲得理學(xué)博士學(xué)位，2016-2017訪問法國馬賽大學(xué)數(shù)學(xué)系。他的研究方向是微分方程與動力系統(tǒng)及其應(yīng)用，特別關(guān)注反應(yīng)擴(kuò)散方程的行波解及傳播問題。盛教授在燃燒、雙穩(wěn)反應(yīng)擴(kuò)散方程的非平面波等方面取得了一些原創(chuàng)性工作，已主持完成多項(xiàng)國家自然科學(xué)基金項(xiàng)目，主要成果發(fā)表在J.Math. Pures Appl., Calc. Var. PDE, J. Differ. Equa等國際知名學(xué)術(shù)期刊上。

Effects of Advection and Diffusion on Principal Eigenvalue of a Periodic-Parabolic Operator

王智誠 蘭州大學(xué)

摘要：In this paper, we investigate the asymptotic behaviours of the principal eigenvalue of linear periodic-parabolic operator with Neumann boundary condition on bounded domain , Specifcally, we study the asymptotic behaviours of principal eigenvalue in the following five cases: (i) with ; (i) with ; (iii) with ; (iv) ; and (v) for fixed . As an application, we use these results to get some threshold-type dynamical results for an epidemic SIS model in time-periodic environment.

報告人簡介：王智誠，蘭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，蘭州大學(xué)“萃英學(xué)者”特聘教授，博士生導(dǎo)師。1994年本科畢業(yè)于西北師范大學(xué)，2007年在蘭州大學(xué)獲理學(xué)博士學(xué)位。主要成果發(fā)表在Arch. Rational Mech. Anal.、JMPA、Trans. AMS、Indiana Univ. Math. J. SIAM J. Math. Anal.、SIAM J. Appl. Math.、Calc. Var. PDE、J. d’Anal. Math.、JDE、Nonlinearity、J. Nonlinear Sci. 等國際知名學(xué)術(shù)期刊上。2010年入選教育部新世紀(jì)優(yōu)秀人才支持計(jì)劃，2011和2019年分別獲得甘肅省自然科學(xué)二等獎，2016年入選甘肅省飛天學(xué)者特聘教授，主持完成多項(xiàng)國家自然科學(xué)基金面上項(xiàng)目。目前擔(dān)任兩個SCI雜志International J. Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的編委（Associate editor）

主辦單位：西安電子科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院