Aramaki, Junichi Existence of solutions for a quasilinear parabolic type equation containing \(p\)-curl system and applications to blow-up and extinction. (English) Zbl 1372.35160 Adv. Differ. Equ. Control Process. 17, No. 2, 117-158 (2016). Summary: We consider a system of quasilinear parabolic-type equations involving the curl operator associated with the Maxwell equations in a multi-connected domain and deal with the system containing \(p\)-curl system. We show the existence and blow-up or extinction of solution, under more general setting. Cited in 3 Documents MSC: 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35K59 Quasilinear parabolic equations 35B44 Blow-up in context of PDEs 35K67 Singular parabolic equations Keywords:quasilinear parabolic type system; \(p\)-curl system; the Maxwell equations PDFBibTeX XMLCite \textit{J. Aramaki}, Adv. Differ. Equ. Control Process. 17, No. 2, 117--158 (2016; Zbl 1372.35160) Full Text: DOI Link