Well-posedness for Bean's critical state model with displacement current

DOI10.1016/j.jmaa.2009.08.024zbMath1181.78003OpenAlexW2062189695MaRDI QIDQ1043528

Frank Jochmann

Publication date: 9 December 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.08.024

zbMATH Keywords

initial-boundary value problemelectromagnetismexistence and uniqueness of solutionsfirst-order systems of PDEs

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Electromagnetic theory (general) (78A25) Initial value problems for systems of linear first-order PDEs (35F40)

Related Items

Maxwell Variational Inequalities in Type-II Superconductivity ⋮ Maxwell quasi-variational inequalities in superconductivity ⋮ A nonlinear hyperbolic Maxwell system using measure-valued functions ⋮ Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity ⋮ Well-posedness theory for electromagnetic obstacle problems

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• Bean's critical-state model as the \(p\rightarrow\infty\) limit of an evolutionary \(p\)-Laplacian equation
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• Asymptotic behavior of electromagnetic waves in nonlinear dielectric media
• Energy decay of solutions to Maxwell's equations with conductivity and polarization
• Magnetization of Hard Superconductors
• A local compactness theorem for Maxwell's equations
• Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
• On a 𝑝-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory