The Stefan problem for the Fisher–KPP equation
Yihong Du,Zongming Guo +1 more
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In this paper, the authors considered the Fisher-KPP problem with a free boundary governed by a one-phase Stefan condition, and established the existence and uniqueness of the weak solution, and through suitable comparison arguments, extended some of the results obtained earlier in Du and Lin (2010) [11] and Du and Guo (2011) to this general case.About:
This article is published in Journal of Differential Equations.The article was published on 2012-08-01 and is currently open access. It has received 128 citations till now. The article focuses on the topics: Stefan problem & Free boundary problem.read more
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Spreading and vanishing in nonlinear diffusion problems with free boundaries
Yihong Du,Bendong Lou +1 more
TL;DR: In this paper, the authors studied nonlinear diffusion problems of the form ut = uxx+f(u) with free boundaries and showed that the omega limit set of every bounded positive solution is determined by a stationary solution.
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Spreading speed revisited: Analysis of a free boundarymodel
TL;DR: This work derives the free boundary condition by considering a "population loss" at the spreading front, and corrects some mistakes regarding the range of spreading speed in [11].
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Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆
Yihong Du,Zongming Guo +1 more
TL;DR: In this paper, a diffusive logistic equation with a free boundary in higher space dimensions and a heterogeneous environment was studied, and the spreading-vanishing dichotomy established in Du and Lin (2010) [10] still holds in the more general and ecologically realistic setting considered here.
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On a Free Boundary Problem for a Two-Species Weak Competition System
Jong-Shenq Guo,Chang-Hong Wu +1 more
TL;DR: In this paper, a weak competition model with a free boundary in a one-dimensional habitat was studied and the authors provided sufficient conditions for spreading success and failure, respectively, and provided an estimate to show that the spreading speed cannot be faster than the minimal speed of traveling wavefront solutions.
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A diffusive logistic model with a free boundary in time-periodic environment☆
TL;DR: In this paper, the authors study the diffusive logistic equation with a free boundary in time-periodic environment and show that the spreading-vanishing dichotomy is retained in time periodic environment, and also determine the spreading speed.
References
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Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
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Random dispersal in theoretical populations.
TL;DR: In this paper, the authors used the random walk problem as a starting point for the analytical study of dispersal in living organisms and applied the law of diffusion to the understanding of the spatial distribution of population density in both linear and two-dimensional habitats.
Related Papers (5)
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary
Yihong Du,Zhigui Lin +1 more
Spreading and vanishing in nonlinear diffusion problems with free boundaries
Yihong Du,Bendong Lou +1 more