A free boundary problem with nonlinear advection and Dirichlet boundary condition

主講人：蔡靜靜 上海電力大學副教授

時間：2024年4月7日10：30

地點：三號樓332室

舉辦單位：數(shù)理學院

主講人介紹：蔡靜靜，上海電力大學數(shù)理學院副教授，上海市優(yōu)青，主要從事反應(yīng)擴散方程自由邊界問題的理論研究，目前已在 European J. Appl. Math.、Nonlinear Anal.、J. Dynam. Differential Equations、Nonlinear Anal. Real World Appl.等國際重要學術(shù)期刊上發(fā)表論文多篇。

內(nèi)容介紹：We study a free boundary problem for Fisher–KPP equation with nonlinear advection on [0,h(t)], which can model the spreading of chemical substances or biological species in the moving region. In this model, the free boundary h(t) indicates the spreading front of the species. Due to some factors (such as the migration of species), the advection is affected by population density. This paper mainly studies the asymptotic behavior of solutions. We prove that, the solution is either spreading (the survival area [0, h(t)] tends to [0, +∞), the solution converges to a stationary solution defined on the half-line), or converging to small steady state ([0, h(t)] goes to a finite interval and the solution converges to a small stationary solution with compacted support), or converging to big steady state ([0, h(t)] tends to a bigger finite interval, the solution converges to a large stationary solution with compacted support). Besides this, we also prove that, when the input of the species is a critical value, the solution is either spreading or in converging to medium steady state. Additionally, we also have two different spreading results. Finally, using traveling semi-wave, we give the spreading speed when spreading happens.