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Journal of Applied Mathematics and Computation

DOI:http://dx.doi.org/10.26855/jamc.2023.03.005

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Initial Boundary Value Problem for Maxwell-Dirac System in the Half Line

Fengxia Liu1, Yitong Pei2,*, Boling Guo3

1Institute of Artificial Intelligence, Beihang University, Beijing, China.

2Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.

3Institute of Applied Physics and Computational Mathematics, Beijing, China.

*Corresponding author: Yitong Pei

Date: March 8,2023 Hits: 321

Abstract

We consider the inhomogeneous Initial-Boundary value problem (IBVP) for the one dimensional Maxwell-Dirac system, which is a difficult and meaningful coupled equation to study. First, from Laplace transform and semigroup theory, we obtain the local well-posedness (LWP) of the system by contraction map, in addition, we give that the bound is independent of time T, and hence obtain the global well-posedness (GWP) with small solutions of the system. Finally, we obtain a sharp estimate in the long time asymptotics result.

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Initial Boundary Value Problem for Maxwell-Dirac System in the Half Line

How to cite this paper:  Fengxia Liu, Yitong Pei, Boling Guo. (2023) Initial Boundary Value Problem for Maxwell-Dirac System in the Half Line. Journal of Applied Mathematics and Computation7(1), 28-52.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.005