| 標題：Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel |
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| 出版（發表）日期 | 2020/07/15 |
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| 作品名稱 | Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel |
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| 作品名稱（其他語言） | |
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| 著者 | Shin-Ichiro Ei; Jong-Shenq Guo; Hiroshi Ishii; Chin-Chin Wu |
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| 著錄名稱、卷期、頁數 | Journal of Mathematical Analysis and Applications 487(2), 124007 |
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| 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. |
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| 關鍵字 | Traveling wave;Wave speed;Nonlocal equation;Sign-changing kernel |
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| 語言 | 英文(美國) |
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| ISSN | 1096-0813 |
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| 期刊性質 | 國外 |
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| 收錄於 | SCI; |
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| 產學合作 | |
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| 通訊作者 | Jong-Shenq Guo |
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| 審稿制度 | 是 |
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| 國別 | 美國 |
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| 公開徵稿 | |
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| 出版型式 | ,電子版,紙本 |
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