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