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TitleA nonlinear hyperbolic Maxwell system using measure-valued functions
Author(s)Miranda, Fernando
Santos, Lisa
KeywordsHyperbolic system
Measure-valued functions
Duality L(p)-L(p)'
Duality L -L ' p p
Issue date1-Jan-2012
JournalJournal of Mathematical Analysis and Applications
Abstract(s)We consider a modified antenna's problem with power-type constitutive laws. This consists in a new nonlinear hyperbolic system that extends a Duvaut-Lions model. Using the Galerkin approximation, properties of the natural functional spaces, and exploring the $L^p$-$L^{p'}$ duality, we prove the existence of solutions, in a generalized sense, passing to the limit in a family of approximated problems and using measure-valued functions. In this process the difficulties in obtaining the necessary a priori estimates for the solutions of the finite-dimensional problems are overcome through the use of bases with special properties related to the model.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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