A class of electromagnetic p-curl systems: blow-up and finite time extinction - Antontsev, Stanislav (2012)
We study a class of $p$-curl systems arising in electromagnetism, for $\frac65 < p < ∞$, with nonlinear source or sink terms. Denoting by $\boldsymbol h$ the magnetic field, the source terms considered are of the form $\boldsymbol h\left(\int_Ω|\boldsymbol h|^2\right)^{\frac{σ-2}{2}}$, with $σ≥1$. Existence of local or global solutions is proved depending on values of $σ$ and $p$. The blow-up of local solutions is also studied. The sink term is of the form $\boldsymbol h\left(\int_Ω|\boldsymbol h|^k\right)^{-λ}$, with $k,λ>0$. Existence and finite time extinction of solutions are proved, for certain values of $k$ and $λ$.