Publicação
A nonlinear hyperbolic Maxwell system using measure-valued functions
| Resumo: | 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. |
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| Autores principais: | Miranda, Fernando |
| Outros Autores: | Santos, Lisa |
| Assunto: | Hyperbolic system Measure-valued functions Duality L(p)-L(p)' Duality L -L ' p p |
| Ano: | 2012 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | 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. |
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