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Stability of planar waves in reaction-diffusion system

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Abstract

This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on ℝn, where n ⩾ 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t → ∞. The convergence is uniform in ℝn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210018, China

    GuangYing Lü

  2. Natural Science Research Center, Harbin Institute of Technology, Harbin, 150080, China

    MingXin Wang

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  1. GuangYing Lü
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  2. MingXin Wang
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Correspondence to GuangYing Lü.

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Lü, G., Wang, M. Stability of planar waves in reaction-diffusion system. Sci. China Math. 54, 1403–1419 (2011). https://doi.org/10.1007/s11425-011-4210-0

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  • DOI: https://doi.org/10.1007/s11425-011-4210-0

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