Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/41293

 Title: Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism Author(s): Antontsev, StanislavMiranda, FernandoSantos, Lisa Keywords: Electromagnetic problemsp(x,t)-curl systemsVariable exponentsBlow-upExtinction in time Issue date: 2016 Publisher: Elsevier Journal: Journal of Mathematical Analysis and Applications Abstract(s): We study a class of $p(x,t)$-curl systems arising in electromagnetism, with a nonlinear source term. Denoting by $\boldsymbol{h}$ the magnetic field, the source term considered is of the form $\lambda\boldsymbol{h}\left( \int_{\Omega}|\boldsymbol{h}|^{2}\right)^{\frac{\sigma-2}{2}}$ where $\lambda\in\{-1,0,1\}$: when $\lambda\in\{-1,0\}$ we consider $0<\sigma\leq2$ and for $\lambda=1$ we have $\sigma\geq1$. We introduce a suitable functional framework and a convenient basis that allow us to apply the Galerkin's method and prove existence of local or global solutions, depending on the values of $\lambda$ and $\sigma$. We study the finite time extinction or the stabilization towards zero of the solutions when $\lambda\in\{-1,0\}$ and the blow-up of local solutions when $\lambda=1$. Type: Article Description: "Available online 22 March 2016" URI: https://hdl.handle.net/1822/41293 DOI: 10.1016/j.jmaa.2016.03.045 ISSN: 0022-247X Publisher version: http://dx.doi.org/10.1016/j.jmaa.2016.03.045 Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat