講演者 | 下條 昌彦 氏(東京都立大学 理学研究科数理科学専攻) |
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講演題目 | Spreading phenomena and convergence to traveling waves of reaction-diffusion systems |
日時 | 令和5年6月27日(火)15:00--17:15 |
場所 | 東京理科大学 神楽坂キャンパス 8 号館 5 階 852 教室&オンライン(Zoom) https://www.tus.ac.jp/info/access/kagcamp.html https://www.tus.ac.jp/info/campus/kagurazaka.html |
講演概要 [PDF] | The aim of this talk is to study the asymptotic behavior of solutions for some reaction-diffusion systems. (1) By an entire solution, we mean a solution of the reaction-diffusion system which is guaranteed to exist for all real-time in the whole Euclidean space. We establish a Liouville-type theorem for the entire solutions of reaction-diffusion systems. Several examples of spreading processes from ecology and epidemiology will be discussed to demonstrate the uses of this Liouville-type theorem. (2) The convergence to a traveling front of reaction-diffusion systems such as predator-prey models will be presented. Our method is general and universal in the sense that it works well for waves in a wide range of reaction-diffusion systems with equal diffusivities. Several examples from ecology and epidemiology will be discussed to illustrate the applications. This is the joint work with Jong-Shenq Guo (Tamkang University), Thomas Giletti (Institut Èlie Cartan de Lorraine), Arnaud Ducrot (Universitè Le Havre Normandie), Amy Poh Ai-Ling (University of Tokyo), and Yu-Shuo Chen (Tamkang University). |