COLOMBINI, Ferruccio; PETKOV, Vesselin; RAUCH, Jeffrey

doi:10.1090/S0002-9939-2011-10885-2

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COLOMBINI, Ferruccio
Dipartimento di Matematica

PETKOV, Vesselin
Institut de Mathématiques de Bordeaux [IMB]

RAUCH, Jeffrey
Department of Mathematics - University of Michigan

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Proceedings of the American Mathematical Society. 2011, vol. 139, n° 6, p. 2163-2173

American Mathematical Society

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We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming waves. With their aid, we construct dissipative boundary conditions and solutions to Maxwell's equations in the exterior of a sphere which decay exponentially as $t \to +\infty$. They are asymptotically disappearing. Disappearing solutions which are identically zero for $t \geq T > 0$ are constructed which satisfy maximal dissipative boundary conditions which depend on time $t$. Both types are invisible in scattering theory.< Réduire

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Incoming and disappearing solutions for Maxwell's equations

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