報告題目：Multidimentional Gelfand-Levitan-Krein Equations and Inverse Hyperbolic Problems
報告時間：2017年9月6日周三下午3：00--5：00
報告地點(diǎn)：西教五416（理學(xué)院）
報告人：謝爾蓋·卡巴尼瀚
報告摘要：Hyperbolic equations describing the wave processes are of great concern in many domains of applied mathematics. Waves come through object and deliver information about its structure to the surface. Solutions of hyperbolic equations can contain non-smooth and singular components. This leads to easier (compared with elliptic and parabolic cases) inversion of the operator. Usually inverse problems for hyperbolic equations are solved by minimizing the residual functional. Iterative method of minimizing the functional requires the solution of the direct (and, perhaps, adjoint) problem for every iteration of the method. In multidimensional case iterative methods for multidimensional inverse problems are very timeconsuming.e will consider several examples, including - Multidimensional nonlinear acoustic inverse problem (S.I. Kabanikhin, A.D. Satybaev, M.A. Shishlenin, 2004)
- Recovering of the Lame parameters and density of the medium (A.S. Alekseev, 1967; V.S. Belonosov, A.S. Alekseev, 1998)
- Solving the GLM-equations for obtaining the solution of the nonlinear Schrodinger equation (D.A. Shapiro, 2011; R.G. Novikov, 2014; S.K. Turitsyn, 2015).
- Method of inverse scattering problem: integrating nonlinear equations (C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, 1967): KdF (1D) and Kadomtcev-Petviashvili (2D, V.E. Zakharov and A.B. Shabat, 1974).
報告人簡介：謝爾蓋·卡巴尼瀚，俄羅斯科學(xué)院通訊院士，現(xiàn)為俄羅斯科學(xué)院西伯利亞分院計算數(shù)學(xué)與數(shù)學(xué)地球物理研究所所長。長期從事數(shù)學(xué)反問題的研究工作，在電磁學(xué)、梯度方法的強(qiáng)收斂性、非線性拋物問題算法設(shè)計、多維Gelfand-Levitan and Krein 方程反問題等諸多問題方面，做出了開創(chuàng)性的工作。
