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Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms

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Abstract

In this paper, we investigate the speed selection mechanism of traveling wave solutions for a reaction–diffusion–advection equation with high-order terms in a cylindrical domain. The study focuses the problem under two cases for Neumann boundary condition and Dirichlet boundary condition. By using the upper and lower solutions method, general conditions for both linear and nonlinear selections are obtained. When the equation is expanded to higher dimensions, literature examining this particular topic is scarce. In light of this, new results have been obtained for both linear and nonlinear speed selections of the equation with high-order terms. For different power exponents m and n, specific sufficient conditions for linear and nonlinear selections with the minimal wave speed are derived by selecting suitable upper and lower solutions. The impact of the power exponents m and n on speed selection is analyzed.

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Funding

The National Nature Science Foundation of China grant (11801263).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hunan First Normal University, Changsha, 410205, Hunan, China

    Chaohong Pan

  2. School of Mathematics and Physics, University of South China, Hengyang, 421001, Hunan, China

    Chaohong Pan, Shulin Hu & Hongyong Wang

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  1. Chaohong Pan
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  2. Shulin Hu
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  3. Hongyong Wang
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Contributions

SH and CP analyzed the method and revised the manuscript text together, and SH wrote and prepared the original draft, HW supervised the writing. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Shulin Hu.

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Pan, C., Hu, S. & Wang, H. Speed Selection of Traveling Waves of a Reaction–Diffusion–Advection Equation with High-Order Terms. Qual. Theory Dyn. Syst. 23, 75 (2024). https://doi.org/10.1007/s12346-023-00923-8

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