主講人：呂克寧教授/杜增吉教授 四川大學(xué)/江蘇師范大學(xué)

時(shí)間：2022年11月5日9：00

地點(diǎn)：騰訊會(huì)議 233 479 353

舉辦單位：數(shù)理學(xué)院

主講人介紹：呂克寧教授，美國(guó)楊伯翰大學(xué)教授，美國(guó)數(shù)學(xué)會(huì)會(huì)士，研究方向?yàn)闊o(wú)窮維動(dòng)力系統(tǒng)、非線(xiàn)性偏微分方程、隨機(jī)偏微分方程，已發(fā)表論文近百篇，發(fā)表期刊包括《Invent. Math.》、《Comm. Pure Appl. Math.》、《Mem. Amer. Math. Soc.》、《Arch. Rational Mech. Anal.》、《Adv. Math.》?，F(xiàn)任《J. Differential Equations》共同主編。 杜增吉教授，江蘇師范大學(xué)副校長(zhǎng)、教授、博士生導(dǎo)師。中國(guó)數(shù)學(xué)會(huì)奇異攝動(dòng)專(zhuān)業(yè)委員會(huì)副理事長(zhǎng)，江蘇省優(yōu)秀教育工作者。研究方向?yàn)槲⒎址匠膛c動(dòng)力系統(tǒng)、奇異攝動(dòng)理論及其應(yīng)用、生物數(shù)學(xué)等。在J. Funct. Anal.，J. Nonlinear Sci., J. Differential Equations, J. Math. Biol.，《中國(guó)科學(xué)數(shù)學(xué)》等期刊上發(fā)表論文70余篇。先后主持國(guó)家自然科學(xué)基金和省部級(jí)項(xiàng)目10余項(xiàng)，獲得江蘇省數(shù)學(xué)成就獎(jiǎng)，江蘇省優(yōu)秀教學(xué)成果獎(jiǎng)，山東省自然科學(xué)獎(jiǎng)二等獎(jiǎng)等。

內(nèi)容介紹：

呂克寧教授報(bào)告摘要：In this talk, we report some recent work on both local theory and global theory of invariant manifolds for infinite dimensional dynamical systems and its applications to partial differential equations. 

杜增吉教授報(bào)告摘要：In this talk, we are concerned with the existence of traveling pulse solutions of one-dimensional generalized Keller-Segel system with nonlinear chemical gradients and small cell diffusion by using the dynamical systems approach. To show the existence of traveling pulse solutions, we first analyze the dynamics of the system by geometric singular perturbation theory. And then we seek an invariant region for the associated traveling wave equation. Finally, we apply Poincare-Bendixson theorem to analyze the flow on this invariant region to obtain the existence of traveling pulse solutions in this bounded invariant region.