Bull. Korean Math. Soc. 2019; 56(6): 1447-1465
Online first article October 16, 2019 Printed November 30, 2019
https://doi.org/10.4134/BKMS.b181077
Copyright © The Korean Mathematical Society.
Meixia Xiao, Xianwen Zhang
Wuhan Textile University; Huazhong University of Science and Technology
In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_{0}$, we prove the existence and uniqueness of the mild solution via the iteration method.
Keywords: Klein-Gordon field, mild solutions, Bessel function, character\-istics
MSC numbers: Primary 35F25, 35J05, 35Q83, 82C40
Supported by: This work is supported by the National Natural Science Foundation of China (Grant No.11871024)
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