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On a singular limit problem for nonlinear Maxwell's equations

Hong-Ming Yin
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Abstract

In this paper we study the following nonlinear Maxwell's equations \\ $\varepsilon \E_{t}+σ(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where $σ(x,s)$ is a monotone graph of $s$. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as $\varepsilon\rightarrow 0$ converges to the solution of quasi-stationary Maxwell's equations.

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Hong-Ming Yin. 1998-04-07. On a singular limit problem for nonlinear Maxwell's equations. https://arxiv.org/abs/math/9804149

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