Entire solution originating from three fronts for a discrete diffusive equation

Chen, Yan Yu

doi:10.5556/j.tkjm.48.2017.2442

Cited by 9 publications

(4 citation statements)

References 16 publications

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“…Recently, there are other new types of entire solutions merging three fronts, which were addressed in [1,3]. Motivated by these works, it is natural and interesting to study new entire solutions merging three fronts of the system (1.1).…”

Section: Introductionmentioning

confidence: 99%

Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system

Gan¹,

Yu²

2019

Preprint

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This paper is concerned with the entire solutions of a two-dimensional nonlocal periodic lattice dynamical system. With bistable assumption, it is well known that the system has three different types of traveling fronts. The existence of merging-front entire solutions originating from two fronts for the system have been established by Dong, Li & Zhang [Comm. Pur Appl. Anal., 17(2018), 2517-2545. Under certain conditions on the wave speeds, and by some auxiliary rational functions with certain properties to construct appropriate super-and sub solutions of the system, we establish two new types of entire solutions which originating from three fronts.

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Section: Introductionmentioning

confidence: 99%

Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system

Gan¹,

Yu²

2019

Preprint

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“…Next, we consider the following four ordinary differential equations with the initial conditions (see [3,7,28]):…”

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confidence: 99%

Novel entire solutions in a nonlocal 2-D discrete periodic media for bistable dynamics

Yu¹,

Yuan²,

Gan³

2021

DCDS-B

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This paper is concerned with novel entire solutions originating from three pulsating traveling fronts for nonlocal discrete periodic system (NDPS) on 2-D Lattices u i,j (t) = k 1 ∈Z\{0} k 2 ∈Z\{0} J(k 1 , k 2) u i−k 1 ,j−k 2 (t) − u i,j (t) + f i,j (u i,j (t)). More precisely, let ϕ i,j;k (icosθ + jsinθ + v k t) (k = 1, 2, 3) be the pulsating traveling front of NDPS with the wave speed v k and connecting two different constant states, then NDPS admits an entire solution u i,j (t), which satisfies lim t→−∞ 1≤k≤3 sup p k−1 (t)≤ξ≤p k (t) |u i,j (t) − ϕ i,j;k (ξ + v k t + θ k)| = 0, where ξ =: i cos θ + j sin θ, v 1 < v 2 < v 3 and θ k (k = 1, 2) is some constant, p 0 = −∞, p k (t) := −(v k + v k+1)t/2 (k = 1, 2) and p 3 = +∞.

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“…Very recently, under certain assumptions on wave speed, some entire solutions originating from three fronts have been constructed by Chen [7] for discrete diffusive equation (3). Further, for the classical reaction-diffusion equation (2), Chen et al [8] established the existence of entire solutions formed by collisions of three or four fronts and the absence of entire solutions resulting from the collisions of five or more fronts.…”

mentioning

confidence: 99%

“…Resolving this issue represents a main contribution of our current study. In order to extend the above work [7,8] to nonlocal dispersal equations (1), we shall study entire solutions u originating from k traveling wave solutions {(c j , φ j ), j =…”

mentioning

confidence: 99%

Entire solutions originating from monotone fronts for nonlocal dispersal equations with bistable nonlinearity

Dong¹,

Li²,

Wu³

et al. 2021

Discrete &Amp; Continuous Dynamical Systems - B

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This paper mainly focuses on the entire solutions of nonlocal dispersal equations with bistable nonlinearity. Under certain assumptions of wave speed, firstly constructing appropriate super-and sub-solutions and applying corresponding comparison principle, we established the existence and related properties of entire solutions formed by the collision of three and four traveling wave solutions. Then by introducing the definition of terminated sequence, it is proved that there has no entire solutions formed by k traveling wave solutions that collide with each other as long as k ≥ 5. Finally, based on the classical weighted energy approach, we obtain the global exponentially stability of the entire solutions in some weighted space.

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Entire solution originating from three fronts for a discrete diffusive equation

Cited by 9 publications

References 16 publications

Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system

Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system

Novel entire solutions in a nonlocal 2-D discrete periodic media for bistable dynamics

Entire solutions originating from monotone fronts for nonlocal dispersal equations with bistable nonlinearity

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