Mild Solutions for the Relativistic Vlasov-Klein-Gordon System
Bull. Korean Math. Soc.
Published online October 16, 2019
Meixia Xiao and Xianwen Zhang
School of Mathematics and Computer Science, Wuhan Textile University, School of Mathematics and Statistics, 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, characteristics
MSC numbers : 35F25, 35J05, 35Q83, 82C40
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