Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4274
Title: Global existence for a quasilinear Maxwell system
Authors: Lucente, Sandra
Ziliotti, Guido
Keywords: Maxwell systemSobolev spaces on manifoldSmall data
Issue Date: 2000
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.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
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 $\left[5\right]$.
Type: Article
URI: http://hdl.handle.net/10077/4274
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2

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