報告題目: The dynamics of a nonlocal dispersal logistic model with seasonal succession
報告時間: 2021年11月25日(星期四), 20:00-21:00
報告地點: 騰訊會議，會議號：180 708 173
內(nèi)容摘要: This talk includes two parts.
The dyanmics of a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat is considered in the first part, where the time periodicity accounts for the effect of two different seasons. By showing the existence and asymptotic profile of the principal eigenvalue of a time-periodic nonlocal dispersal operator, and applying the time-periodic upper-lower solution method, we obtain the criteria for persistence or extinction of species. Moreover, the limiting profile of positive time-periodic solution is presented here.
The second part of this talk focuses on the free boundary problem of a nonlocal dispersal logistic model with seasonal succession, where the free boundaries $x=g(t),x=h(t)$ represent the expanding front. We prove the existence and uniqueness of global solution, and then examine the long-time dynamical behaviour and the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model without seasonal succession. Moreover, we use a“thin-tail” condition on the kernel function to estimate the asymptotic speeds of $(g,h)$ and the asymptotic spreading speed of $u$, which is achieved by solving the associated semi-wave problem.
報告人簡介: 戴斌祥，中南大學數(shù)學與統(tǒng)計學院二級教授、博士生導師；湖南省數(shù)學學會常務(wù)理事、高等教育與大學數(shù)學競賽工作委員會副主任委員；中國生物數(shù)學會常務(wù)理事；入選湖南省新世紀121人才工程人選；主要從事時滯微分方程與離散動力系統(tǒng)、種群生態(tài)學與傳染病學、反應(yīng)擴散方程的定性理論與應(yīng)用等領(lǐng)域的研究，先后在《Nonlinearity》、《J. Dyn. Diff. Equ.》、《Chaos》、《Appl. Math. Model》等國內(nèi)外權(quán)威期刊上發(fā)表學術(shù)論文150多篇，主持5項國家自然科學基金面上項目、1項國家973計劃子課題、1項湖南省自然科學基金重點項目和多項省部級科研課題，獲得湖南省科技進步一等獎和湖南省自然科學一等獎各1項，主編出版教材6部，2020年獲得寶鋼教育基金優(yōu)秀教師獎。
歡迎感興趣的老師和同學參加！
