Mild solutions for the relativistic Vlasov-Klein-Gordon system Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1447-1465 https://doi.org/10.4134/BKMS.b181077 Published online October 16, 2019 Printed November 30, 2019 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) Downloads: Full-text PDF   Full-text HTML