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Global existence for a quasilinear Maxwell system
Lucente, Sandra
Ziliotti, Guido
2000
Abstract
In this work we deal with quasilinear Maxwell system
\[
\begin{cases}
\overset{\partial t\left(\epsilon_{0}E+\Phi\left(E\right)\right)=curl\: H,}{\partial_{t}H=-curlE,}\end{cases}
\]
where $\epsilon_{0}$=diag $\left(a^{2},b^{2},b^{2}\right)$ is a
diagonal matrix and $\Phi$ is a smooth matrix such that $\mid\Phi\mid$
has polynomial growth near E = O. Under suitable hypotheses on $\Phi$
we establish a global existence result for small amplitude solutions.
The main argument is the study of pseudo-differential equations obtained
diagonalizing the system and using for these equations a particular
von Wahl-type estimate described in our previous paper $\left[5\right]$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Sandra Lucente and Guido Ziliotti, "Global existence for a quasilinear Maxwell system", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.2, pp. 169-187.
Languages
en
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