数値解析・応用解析セミナー

7月26日(木)  16:30 -- 17:30 Vladimir Romanov (Sobolev Institute of mathematics, Novosibirsk, Russia)
             ``Phaseless inverse problems for Maxwell equations''


＜研究発表要旨＞
Under consideration is the stationary system of equations of electrodynamics 
relating to a nonmagnetic nonconducting medium. We study the problem of 
recovering the permittivity coefficient $\verepsilon$ from given vectors 
of electric or magnetic intensities of the electromagnetic field. It is 
assumed that the field is generated by a point impulsive dipole located 
at some point y. It is also assumed that the permittivity differs from 
a given constant $\verepsilon_0$ only inside some compact domain 
$\Omega \subset R^3$  with smooth boundary S. To recover $\verepsilon$" 
inside $\Omega$, we use the information on a solution to the corresponding 
direct problem for the system of equations of electrodynamics on the whole 
boundary of $\Omega$ for all frequencies from some fixed frequency $\omega_0$
on and for all y $\in$ S. The asymptotics of a solution to the direct problem 
for large frequencies is studied and it isdemonstrated that this information 
allows us to reduce the initial problem to the well-known inverse kinematic 
problem of recovering the refraction index inside $\Omega$ with given travel 
times of electromagnetic waves between two arbitrary points on the boundary 
of $\Omega$. This allows us to state uniqueness theorem for solutions to 
the problem in question and opens up a way of its constructive solution.


●セミナー室: 京都大学 総合研究12号館 2階203号室
            （応用解析学講座セミナー室）

●総合研究12号館はキャンパスマップでは「京都大学本部構内 54番建物」です。
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セミナー連絡先: 京都大学大学院 情報学研究科 先端数理科学専攻
                 磯 祐介    e-mail; iso@i.kyoto-u.ac.jp