Global stability of curved fronts in the Belousov–Zhabotinskii reaction–diffusion system in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si2.gif"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>

Niu, Hong-Tao; Bu, Zhen-Hui; Wang, Zhicheng

doi:10.1016/j.nonrwa.2018.10.003

Cited by 15 publications

(9 citation statements)

References 47 publications

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In this article, we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. The existence and stability of V-shaped traveling fronts for the BZ system in R 2 had been proved in our previous papers [30,31]. Here we establish the existence and stability of pyramidal traveling fronts for the BZ system in R 3 .

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confidence: 52%

Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3

Ma,

Niu,

Wang

2020

ejde

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In this article, we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. The existence and stability of V-shaped traveling fronts for the BZ system in $\mathbb{R}^2$ had been proved in our previous papers [30, 31]. Here we establish the existence and stability of pyramidal traveling fronts for the BZ system in $\mathbb{R}^3$. For more information see https://ejde.math.txstate.edu/Volumes/2020/112/abstr.html

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confidence: 52%

Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3

Ma,

Niu,

Wang

2020

ejde

Self Cite

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In this article, we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. The existence and stability of V-shaped traveling fronts for the BZ system in $\mathbb{R}^2$ had been proved in our previous papers [30, 31]. Here we establish the existence and stability of pyramidal traveling fronts for the BZ system in $\mathbb{R}^3$. For more information see https://ejde.math.txstate.edu/Volumes/2020/112/abstr.html

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“…⎧ ⎨ ⎩ Then, a two-point boundary value problem can be constructed as follows 13), and  a is defined as…”

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confidence: 99%

“…A lot of progress has been made, mainly focused on the existence, asymptotic behavior, stability and propagation speed of traveling wave solutions [4][5][6][7][8][9]. For the study of high-dimensional cases, refer to [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Traveling wave solution for a nonlocal Belousov-Zhabotinskii reaction-diffusion system

Chang,

Han,

Yang

2024

Phys. Scr.

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We consider a Belousov-Zhabotinskii reaction-diﬀusion system with nonlocal eﬀects and study the existence of traveling wave solutions. By constructing appropriate super- and sub-solutions and using Schauder’s ﬁxed point theorem, we show that there is a critical speed c > 0 such that when the wave speed c > c , there exists a traveling wave solution connecting (0, 0) to an unknown positive steady-state, while there is no travelling wave solution when c < c . Moreover, we also examine a special case where ϕ1(x) is Dirac function, and demonstrate the existence of the traveling wave solution connecting the equilibria (0, 0) and (1, 1) for c > c , whereas the traveling wave solution does not exist when c < c . Finally, the long-time behavior of the solution is investigated through numerical simulation and theoretical analysis, and it is found that the choice of kernel functions and the setting of initial value conditions play a crucial role.

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“…On the other hand, for non-planar traveling waves, Brazhnik and Davydov [9] predicted the existence of V -shaped traveling waves in the Belousov-Zhabotinskii system, which were subsequently verified by Pérez-Muñuzuri et al [43] in experiments. Later, a mathematical verification of the existence and stability of V -shaped traveling waves in R 2 were presented in [38,39]. Subsequently, the results of pyramidal traveling waves in R 3 were established in [34].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the standard pyramidal traveling waves no longer exist anymore in such domains, the analysis of the propagation properties of the solutions of (1.1) is more complex than that in the whole space R N . It is worth noting that the proof in this paper mainly relies on the construction of the super-and sub-solutions, which are inspired by [38,40,51,55].…”

Section: Introductionmentioning

confidence: 99%

Pyramidal traveling waves for a Belousov-Zhabotinskii system with obstacles

Han,

Chang

2023

Preprint

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This paper is concerned with pyramidal traveling waves for Belousov-Zhabotinskii reaction-diffusion system in external domains $\Omega=\mathbb{R}^N\backslash K$ with a compact obstacle $K$ and aims to investigate the large time dynamics of an entire solution emanating from a pyramidal traveling wave. By constructing several super- and sub-solutions with desirable characteristics, some favorable properties of the pyramidal traveling wave are obtained. We show that by providing propagation completely of the entire solution, the pyramidal traveling wave will converge to the same shape of the pyramidal traveling wave after far behind the obstacle. AMS Subject Classification (2010): 35A18, 35B08, 35C07, 35K57

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Global stability of curved fronts in the Belousov–Zhabotinskii reaction–diffusion system in R2

Cited by 15 publications

References 47 publications

Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3

Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3

Traveling wave solution for a nonlocal Belousov-Zhabotinskii reaction-diffusion system

Pyramidal traveling waves for a Belousov-Zhabotinskii system with obstacles

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