A class of electromagnetic p-curl systems: blow-up and finite time extinction

• Autor(a) principal: Antontsev, Stanislav
• Data de Publicação: 2012
• Outros Autores: Miranda, Fernando, Santos, Lisa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/19019
• topic: Electromagnetic problems; p-curl systems; Blow-up; Extinction in time; Science & Technology

We study a class of $p$-curl systems arising in electromagnetism, for $\frac65 < p < \infty$, with nonlinear source or sink terms. Denoting by $\boldsymbol h$ the magnetic field, the source terms considered are of the form $\boldsymbol h\left(\int_\Omega|\boldsymbol h|^2\right)^{\frac{\sigma-2}{2}}$, with $\sigma\geq1$. Existence of local or global solutions is proved depending on values of $\sigma$ and $p$. The blow-up of local solutions is also studied. The sink term is of the form $\boldsymbol h\left(\int_\Omega|\boldsymbol h|^k\right)^{-\lambda}$, with $k,\lambda>0$. Existence and finite time extinction of solutions are proved, for certain values of $k$ and $\lambda$.