On a singular limit problem for nonlinear Maxwell's equations

Details On a singular limit problem for nonlinear Maxwell's equations On a singular limit problem for nonlinear Maxwell's equations

1998-04-07

arxiv.org/abs/math/9804149v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study the following nonlinear Maxwell's equations \\ $\varepsilon \E_{t}+\sigma(x,|\E|)\E= \g \vh +\F,\, \vh_{t}+\g \E=0$, where $\sigma(x,s)$ 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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