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, SandraZiliotti, Guido Keywords: Maxwell systemSobolev spaces on manifoldSmall 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 Mathematics31 (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: 35Q6035F25 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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