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Article
Pulsating waves and entire solutions for a spatially periodic nonlocal dispersal system with a quiescent stage
This paper deals with the pulsating waves and entire solutions for a spatially periodic nonlocal dispersal model with a quiescent stage. By the method of super- and subsolutions together with the comparison pr...
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Article
Entire solution in an ignition nonlocal dispersal equation: Asymmetric kernel
This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here. The asymme...
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Article
Existence, uniqueness and stability of pyramidal traveling fronts in reaction-diffusion systems
In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fron...
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Article
Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling front...
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Article
Entire solutions in reaction-advection-diffusion equations with bistable nonlinearities in heterogeneous media
This paper is concerned with entire solutions (t ∈ ℝ) for bistable reaction-advection-diffusion equations in heterogeneous media. By using traveling curved fronts connecting a constant unstable stationary state a...
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Article
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in ℝ2. We first establish the existence of traveling wavefronts as well as their precise asympto...