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

• Author(s): Antontsev, Stanislav ; Miranda, Fernando ; Santos, Lisa
• Date: 2012
• Persistent ID: http://hdl.handle.net/1822/19019
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Electromagnetic problems; p-curl systems; Blow-up; Extinction in time
• Document Type: Article
• Language: English

Description

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 $\lambda$.