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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 system
Sobolev spaces on manifold
Small data
Issue Date: 2000
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: 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 $\left[5\right]$.
URI: http://hdl.handle.net/10077/4274
ISSN: 0049-4704
MS Classification: 35Q60
35F25
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