Incoming and disappearing solutions for Maxwell's equations
Language
en
Article de revue
This item was published in
Proceedings of the American Mathematical Society. 2011, vol. 139, n° 6, p. 2163-2173
American Mathematical Society
English Abstract
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 ...Read more >
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.Read less <
Origin
Hal imported