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

TitleBlow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism
Author(s)Antontsev, Stanislav
Miranda, Fernando
Santos, Lisa
KeywordsElectromagnetic problems
p(x,t)-curl systems
Variable exponents
Blow-up
Extinction in time
Issue date2016
PublisherElsevier
JournalJournal 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 $\lambda=1$.
TypeArticle
Description"Available online 22 March 2016"
URIhttp://hdl.handle.net/1822/41293
DOI10.1016/j.jmaa.2016.03.045
ISSN0022-247X
Publisher versionhttp://dx.doi.org/10.1016/j.jmaa.2016.03.045
Peer-Reviewedyes
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

Files in This Item:
File Description SizeFormat 
AntontsevMirandaSantos2016RepositoriUM.pdf494,28 kBAdobe PDFView/Open

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu ORCID