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Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems
TLDR
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Expand
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Long time behavior of solutions of Fisher-KPP equation with advection and free boundaries
We consider Fisher-KPP equation with advection: $u_t=u_{xx}-\beta u_x+f(u)$ for $x\in (g(t),h(t))$, where $g(t)$ and $h(t)$ are two free boundaries satisfying Stefan conditions. This equation is usedExpand
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A KPP road–field system with spatially periodic exchange terms
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 systemExpand
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Asymptotic Behavior of Solutions of a Reaction Diffusion Equation with Free Boundary Conditions
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))+αExpand
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Semi-wave and spreading speed for the diffusive competition model with a free boundary
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 sphericallyExpand
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Long time behavior of solutions of a reaction–diffusion equation on unbounded intervals with Robin boundary conditions ☆
We study the long time behavior, as $t\to\infty$, of solutions of $$ \left\{ \begin{array}{ll} u_t = u_{xx} + f(u), & x>0, \ t >0,\\ u(0,t) = b u_x(0,t), & t>0,\\ u(x,0) = u_0 (x)\geqslant 0 ,Expand
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Spreading speed and profile for nonlinear Stefan problems in high space dimensions
We consider nonlinear diffusion problems of the form ut=Δu+f(u) with Stefan type free boundary conditions, where the nonlinear term f(u) is of monostable, bistable or combustion type. Such problemsExpand
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Fisher–KPP equation with free boundaries and time-periodic advections
We consider a reaction–diffusion–advection equation of the form: $$u_t=u_{xx}-\beta (t)u_x+f(t,u)$$ut=uxx-β(t)ux+f(t,u) for $$x\in (g(t),h(t))$$x∈(g(t),h(t)), where $$\beta (t)$$β(t) is a T-periodicExpand
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Long time behavior for solutions of the diffusive logistic equation with advection and free boundary
We consider the influence of a shifting environment and an advection on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When theExpand
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Nonlinear Diffusion Problems with Free Boundaries: Convergence, Transition Speed, and Zero Number Arguments
TLDR
This paper continues the investigation of the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$. Expand
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