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- Yihong Du, Hiroshi Matsuzawa, Maolin Zhou
- SIAM J. Math. Analysis
- 2014
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free… (More)
- Haowei Gu, Bendong Lou, Maolin Zhou
- 2015
We consider Fisher-KPP equation with advection: ut=uxx−βux+f(u) for x∈(g(t),h(t)), where g(t) and h(t) are two free boundaries satisfying Stefan conditions. This equation is used to describe the… (More)
- Yihong Du, Bendong Lou, Maolin Zhou
- SIAM J. Math. Analysis
- 2015
This paper continues the investigation of Du and Lou (J. European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form… (More)
We study a nonlinear diffusion equation of the form $$u_t=u_{xx}+f(u)\ (x\in [g(t),h(t)])$$ut=uxx+f(u)(x∈[g(t),h(t)]) with free boundary conditions $$g'(t)=-u_x(t,g(t))+\alpha $$g′(t)=-ux(t,g(t))+α… (More)
- Yihong Du, Mingxin Wang, Maolin Zhou
- 2015
Abstract We determine the asymptotic spreading speed of an invasive species, which invades the territory of a native competitor, governed by a diffusive competition model with a free boundary in a… (More)
Abstract We consider nonlinear diffusion problems of the form u t = Δ u + f ( u ) with Stefan type free boundary conditions, where the nonlinear term f ( u ) is of monostable, bistable or combustion… (More)
We take interest in a reaction-diffusion system which has been recently proposed [11] as a model for the effect of a road on propagation phenomena arising in epidemiology and ecology. This system… (More)
- Rui Peng, Maolin Zhou
- 2016
In this article, we study, as the coefficient $s\to\infty$, the asymptotic behavior of the principal eigenvalue of $$-\varphi''(x)-2sm'(x)\varphi'(x)+c(x)\varphi(x)=\lambda_s\varphi(x),\ \ 0<x<1,$$… (More)
We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in… (More)