教師資料查詢 | 類別: 期刊論文 | 教師: 郭忠勝 Guo, Jong-shenq (瀏覽個人網頁)

標題:Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
學年108
學期2
出版(發表)日期2020/07/15
作品名稱Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
作品名稱(其他語言)
著者Shin-Ichiro Ei; Jong-Shenq Guo; Hiroshi Ishii; Chin-Chin Wu
單位
出版者
著錄名稱、卷期、頁數Journal of Mathematical Analysis and Applications 487(2), 124007
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.
關鍵字Traveling wave;Wave speed;Nonlocal equation;Sign-changing kernel
語言英文(美國)
ISSN1096-0813
期刊性質國外
收錄於SCI;
產學合作
通訊作者Jong-Shenq Guo
審稿制度
國別美國
公開徵稿
出版型式,電子版,紙本
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