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 en_US
ISSN 1096-0813
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 是
國別 USA
公開徵稿
出版型式 ,電子版,紙本
相關連結

機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/118761 )