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| In this talk, we concern with a free boundary problem of nonlinear advection-diffusion problem in one space dimension. We assume that the nonlinear term is monostable, bistable or combustion type. Such problems may be used to describe the spreading of a biological or chemical species under an advective environment.
Du and Lou(to appear) considered the problem without advection term and studied the long-time dynamical behavior of solutions ({\bf spreading} and {\bf vanishing}) and determined the asymptotic spreading speed of the free boundaries when spreading happens. Du, Matsuzawa and Zhou (2014) obtained a sharper estimate for the spreading speed of the fronts than that in [Du-Lou], and they show that the solution approaches the semi-wave when spreading happens.
For the problem with the advection term, Gu, Lin and Lou(to appear) considered the problem in the case where the nonlinear term is the logistic type and showed that when spreading happens, the rightward and leftward asymptotic spreading speeds are different due to the advection term.
The aim of this talk is to give a much sharper estimate for the spreading speed of the fronts than that in [Gu-Lin-Lou], and obtain how the solution approaches the semi-wave when spreading happens. |
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