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 system; Sobolev spaces on manifold; Small 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 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 adiagonal 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 obtaineddiagonalizing the system and using for these equations a particularvon 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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