Plane waves in nonlinear electromagnetism

DOI10.1016/0167-2789(88)90078-4zbMath0736.35133OpenAlexW2012633450MaRDI QIDQ1813137

Denis Serre

Publication date: 25 June 1992

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(88)90078-4

zbMATH Keywords

existencewave propagationCauchy problemweak solutionsnonlinear Maxwell equationssymmetrisable system

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) First-order nonlinear hyperbolic equations (35L60)

Related Items (13)

Symmetric divergence-free tensors in the calculus of variations ⋮ Géométrie des systèmes hyperboliques de lois de conservation ⋮ An exact description of nonlinear wave interaction processes ruled by \(2\times 2\) hyperbolic systems ⋮ Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences ⋮ Case study of a nonlinear, nonconservative, nonstrictly hyperbolic system ⋮ Lagrangian flows and the one-dimensional Peano phenomenon for ODEs ⋮ Nonlinear oscillations of hyperbolic systems: Methods and qualitative results ⋮ Multivalued solutions to some nonlinear and non-strictly hyperbolic systems ⋮ The method of quasidecoupling for discontinuous solutions to conservation laws ⋮ Vanishing viscosity with short wave-long wave interactions for systems of conservation laws ⋮ Non-uniformity of vanishing viscosity approximation ⋮ Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness ⋮ Convergent perturbative power series solution of the stationary Maxwell–Born–Infeld field equations with regular sources

Cites Work

• Convergence of approximate solutions to conservation laws
• La compacité par compensation pour les systèmes hyperboliques nonlinéaires de deux équations à une dimension d'espace. (Compensated compactness for 2\(\times 2\) hyperbolic systems of conservation laws)
• Thermodynamic restrictions on the constitutive equations of electromagnetic theory
• Hyperbolic systems of conservation laws II
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