Cauchy problem for the nonlinear Klein–Gordon equation coupled with the Maxwell equation

In this paper, we study the nonlinear Klein–Gordon equation coupled with a Maxwell equation. Using the energy method, we obtain a local existence result for the Cauchy problem.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2016-11, Vol.443 (2), p.778-796
Main Authors: Colin, Mathieu, Watanabe, Tatsuya
Format: Article
Language:English
Subjects:
Analysis of PDEs
Cauchy problem
Energy method
Klein–Gordon–Maxwell system
Mathematics
Symmetric hyperbolic system
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Description
Summary:In this paper, we study the nonlinear Klein–Gordon equation coupled with a Maxwell equation. Using the energy method, we obtain a local existence result for the Cauchy problem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.05.057