数値解析・応用解析セミナー 3月8日(木) 15:00 -- 16:00 川越 大輔(京都大学情報学研究科) ``Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the diffused optical tomography.'' <研究発表要旨> In this talk, we consider a boundary value problem of the stationary transport equation with the incoming boundary condition in a two or three dimensional bounded convex domain, and we describe discontinuity of the solution arising from discontinuous points of the incoming boundary data, which we call the boundary-induced discontinuity. In particular, we show propagation of the boundary-induced discontinuity along a positive characteristic line starting from the discontinuous point of the incoming boundary data and also show the exponential decay of the jump of the solution on a discontinuous point under suitable assumptions. The exponential decay gives an idea for solving an inverse problem to determine an unknown coefficient in the stationary transport equation from boundary measurement. We remark the inverse problem is related to the diffused optical tomography, which is a new medical imaging technology. ●セミナー室: 京都大学 総合研究12号館 2階203号 (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