Mild solutions for the relativistic Vlasov-Klein-Gordon system
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1447-1465
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)
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