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Existence of global solutions to one-dimensional nonlinear Maxwell’s equations

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Abstract

1-D nonlinear Maxwell’s equations are expressed as a 2 × 2 system of hyperbolic conservation laws which is linearly degenerate onw j =0 (w j :j-th Riemann invariant). Employing Glimm’s difference scheme, we show the global existence of a weak solution for the initial data the total variation of which is sufficiently small.

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Authors and Affiliations

  1. School of Economics, Otemon-Gakuin University, 2-1-15 Nishiai, 567, Ibaraki, Osaka, Japan

    Fumioki Asakura

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  1. Fumioki Asakura
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Asakura, F. Existence of global solutions to one-dimensional nonlinear Maxwell’s equations. Japan J. Appl. Math. 7, 399–421 (1990). https://doi.org/10.1007/BF03167851

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  • DOI: https://doi.org/10.1007/BF03167851

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