Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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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.

Mild solutions for the relativistic Vlasov-Klein-Gordon system

Meixia Xiao, Xianwen Zhang

Wuhan Textile University; Huazhong University of Science and Technology

Abstract

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)