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Abstract:
We consider the Fisher-KPP equation with advection $u_t = u_{xx} - \beta u_x + f(u)$ in a one dimensional varying domain $[g(t), h(t)]$, where $g(t)$ and $h(t)$ are two free boundaries evolving by one-phase Stefan conditions. This equation is used to describe the population dynamics in advective environments. We study the influence of the advection coefficient $\beta$ on the long time behavior of the solutions. We find two critical parameters $c_0$ and $\beta^*$ with $\beta^* > c_0 > 0$ ($c_0$ is the minimal speed of the traveling waves of Fisher-KPP equation) such that the dynamics of the solutions are quite different when $\beta$ belongs to different parameter intervals: $[0,c_0)$, $\{c_0\}$, $(c_0, \beta^*)$ and $[\beta^*, \infty)$. (joint work with Hong Gu and Maolin Zhou).
Biography:
Prof. Bengdong Lou holds his Ph.D. from Shandong University in 1997. Now he is a Professor of Department of Mathematics in Tongji University. Prof. Lou’s current research interest is Qualitative research on the reaction diffusion equations with free boundaries. His work has appeared in the journals: J. Eur. Math. Soc., Ann. I. H. Poincare, SIAM J. Math. Anal., J. Funct. Anal., Commu. PDE, JDE etc.