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。 ------------------------------------------------------------- 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