A class of electromagnetic \(p\)-curl systems: blow-up and finite time extinction

DOI10.1016/j.na.2012.02.011zbMath1246.35102OpenAlexW2102086874MaRDI QIDQ414511

Fernando Miranda, Lisa Santos, Stanislav N. Antontsev

Publication date: 11 May 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1822/19019

zbMATH Keywords

blow upextinction in time\(p\)-curl systemselectromagnetic problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Maxwell equations (35Q61)

Related Items (8)

Blow-up and finite time extinction for \(p(x,t)\)-curl systems arising in electromagnetism ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems without the Ambrosetti-Rabinowitz condition ⋮ Properties of a quasi-uniformly monotone operator and its application to the electromagnetic \(p\)-curl systems. ⋮ Hyperbolic Maxwell variational inequalities of the second kind ⋮ Existence of two solutions for \(p(x)\)-curl systems with a small perturbation ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems arising in electromagnetism ⋮ Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity ⋮ Existence of solutions for systems arising in electromagnetism

Cites Work

• Unnamed Item
• Unnamed Item
• Localization of solutions of anisotropic parabolic equations
• On a \(p\)-curl system arising in electromagnetism
• \(L^p\)-theory for vector potentials and Sobolev's inequalities for vector fields
• Extinction of solutions of parabolic equations with variable anisotropic nonlinearities
• Blow-up of solutions to parabolic equations with nonstandard growth conditions
• Vanishing solutions of anisotropic parabolic equations with variable nonlinearity
• Compact sets in the space \(L^ p(0,T;B)\)
• A CLASS OF STATIONARY NONLINEAR MAXWELL SYSTEMS
• Energy methods for free boundary problems. Applications to nonlinear PDEs and fluid mechanics

This page was built for publication: A class of electromagnetic \(p\)-curl systems: blow-up and finite time extinction