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Existence of solutions for a quasilinear parabolic type equation containing \(p\)-curl system and applications to blow-up and extinction. (English) Zbl 1372.35160

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.

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
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