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TitleA class of electromagnetic p-curl systems: blow-up and finite time extinction
Author(s)Antontsev, Stanislav
Miranda, Fernando
Santos, Lisa
KeywordsElectromagnetic problems
p-curl systems
Extinction in time
Issue dateJun-2012
JournalNonlinear Analysis: Theory, Methods & Applications
Abstract(s)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 $\lambda$.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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