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Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations

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Abstract

This paper studies the multidimensional stability of traveling fronts in monostable reaction-diffusion equations, including Ginzburg-Landau equations and Fisher-KPP equations. Eckmann andWayne (1994) showed a one-dimensional stability result of traveling fronts with speeds c ⩽ c * (the critical speed) under complex perturbations. In the present work, we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions (n = 2, 3), employing weighted energy methods.

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Authors and Affiliations

  1. Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

    HuiHui Zeng

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  1. HuiHui Zeng
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Correspondence to HuiHui Zeng.

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Zeng, H. Multidimensional stability of traveling fronts in monostable reaction-diffusion equations with complex perturbations. Sci. China Math. 57, 353–366 (2014). https://doi.org/10.1007/s11425-013-4617-x

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  • DOI: https://doi.org/10.1007/s11425-013-4617-x

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