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    题名: Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
    作者: Ei, Shin-Ichiro;Guo, Jong-Shenq;Ishii, Hiroshi;Wu, Chin-Chin
    关键词: Traveling wave;Wave speed;Nonlocal equation;Sign-changing kernel
    日期: 2020-07-15
    上传时间: 2020-06-04 12:10:20 (UTC+8)
    出版者: Academic Press
    摘要: In this paper, we study the existence of traveling wave solutions connecting two constant states to a nonlocal scalar equation with sign-changing kernel. A typical example of such kernel in the neural fields is the Mexican hat type function. We first introduce a new notion of upper-lower-solution for the equation of wave profile for a given wave speed. Then, with the help of Schauder's fixed point theorem, we construct two different pairs of upper-lower-solutions to obtain traveling waves for a continuum of wave speeds under two different assumptions. Due to the sign-changing nature of the kernel, the wave profiles may take both positive and negative values. Finally, we analyze the limit of the right-hand tail of wave profiles. Under some further condition on the wave speeds, we prove that the right-hand tail limit of the wave profile does exist. In particular, we obtain the existence of nonnegative traveling waves connecting the unstable state 0 and the stable state 1 for wave speeds large enough.
    關聯: Journal of Mathematical Analysis and Applications 487(2), 124007
    DOI: 10.1016/j.jmaa.2020.124007
    显示于类别:[數學學系暨研究所] 期刊論文

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