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Existence globale d’ondes planes en électromagnétisme non linéaire. (Existence in the large of nonlinear electromagnetic waves). (French) Zbl 0621.35060

The author considers systems where there is an arbitrary form of electromagnetic energy density W(B,D) B and D being the magnetic induction and electric displacement respectively. The magnetic intensity and electric field are \(H_ i=\partial W/\partial B_ i\), \(E_ i=\partial W/\partial D_ i\) respectively.
He states a number of theorems concerning the possible existence of plane transverse electromagnetic waves. The proofs are inadequate, depending on results quoted elsewhere.
Reviewer: Ll.G.Chambers

MSC:

35L20 Initial-boundary value problems for second-order hyperbolic equations
78A40 Waves and radiation in optics and electromagnetic theory
35Q99 Partial differential equations of mathematical physics and other areas of application
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