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The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor
In this paper we consider the diffusive competition model consisting of an invasive species with density $u$ and a native species with density $v$, in a radially symmetric setting with free boundary.Expand
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Blow-up Estimates of the Positive Solution of a Parabolic System
This paper establishes the blow-up estimates for the systems ut − Δu = 0, vt − Δv = 0 in BR × (0, T), BR ⊂ Rn, with the nonlinear boundary conditions ∂u∂η=um1vn1 and ∂v∂η=um2vn2 on SR × (0, T) whereExpand
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A free boundary problem for a predator–prey model
This article is concerned with a system of semilinear parabolic equations with a free boundary, which arises in a predator–prey ecological model. The conditions for the existence and uniqueness of aExpand
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Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary
In this paper, a reaction–diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on aExpand
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The spreading fronts of an infective environment in a man-environment-man epidemic model
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of anExpand
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Coupled diffusion systems with localized nonlinear reactions
This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit − Δui = upii+1(x0, t), (i = 1, …, k, uk+1 := u1) in Ω × (0, T) with boundaryExpand
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Global existence and blowup of a nonlocal problem in space with free boundary
Abstract This paper concerns a double fronts free boundary problem for the reaction–diffusion equation with a nonlocal nonlinear reaction term in space. For such a problem, we mainly study the blowupExpand
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The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions
Abstract. This paper deals with the blow-up properties of solutions to semilinear heat equation $u_t-u_{xx}=u^p \text{ in }(0,1)\times(0,T)$ with the nonlinear boundary conditions Expand
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Instability induced by cross-diffusion in reaction–diffusion systems
Abstract In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions forExpand
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Different asymptotic spreading speeds induced by advection in a diffusion problem with free boundaries
In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (thatExpand
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