Geodesic
A uniqueness theorem for the inverse problem for the integrodifferential electrodynamics equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 77-86

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The problem of finding a kernel and the index of dielectric permeability for the system of integro-differential equations of electrodynamics with wave dispersion is studied. We consider a direct problem in which the external pulse current is a dipole located at a point $y$ on the boundary $\partial B$ of the unit ball $B$. The point $y$ runs over the whole boundary and is a parameter of the problem. The information available about the solution to the direct problem is the trace on $\partial B$ of the solution to the Cauchy problem given for the time moments close to the time when a wave from the dipole source arrives at the point $x$. The main result is a uniqueness theorem for the solution of the inverse problem.
Keywords: electrodynamics, inverse problem, uniqueness.
Mots-clés : dispersion 
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     author = {A. L. Nazarov and V. G. Romanov},
     title = {A uniqueness theorem for the inverse problem for the integrodifferential electrodynamics equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {77--86},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a7/}
}
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A. L. Nazarov; V. G. Romanov. A uniqueness theorem for the inverse problem for the integrodifferential electrodynamics equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 77-86. http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a7/