A class of electromagnetic [formula omitted]-curl systems: Blow-up and finite time extinction

Abstract

We study a class of p-curl systems arising in electromagnetism, for 65<p<∞, with nonlinear source or sink terms. Denoting by h the magnetic field, the source terms considered are of the form h(∫Ω∣h∣2)σ−22, 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 h(∫Ω∣h∣k)−λ, with k,λ>0. Existence and finite time extinction of solutions are proved, for certain values of k and λ.