Colloquium

Inverse kinematic and integral geometry problems and their applications

  • Speaker: V.G. Romanov (Sobolev Institute of Mathematics)

  • Time: Jul 5, 2022, 10:00-11:00

  • Location: Zoom ID 927 4245 7061, Passcode 220705

Abstract


In my talk I give posing an inverse kinematic problem as problem of recovering the conformal Riemannian metric in a compact domain Ω from Riemannian distances between arbitrary points of the boundary of Ω. With physical point of view this problem consists in recovery a speed in Ω from given travel time τ (x, y) between arbitrary points x and y belonging to ∂Ω. A stability estimate of solutions of this problem is given. Then I introduce an integral geometry problem that consists in recovering a function from its integral along a family of geodesic line of the conformal Riemannian metric. A stability estimate of solutions of this problem is also given. As an application of the considered problems, an acoustic tomography problem is discussed. In this problem 3 unknown coefficients need to be found, namely, a speed of the sound c(x), an attenuation σ(x) and a density ρ(x). It is demonstrated that, under some convenient information about solutions of a forward problem, the recovering c(x) is reduced to the inverse kinematic problem and recovering σ(x) and ρ(x) is reduced to some integral geometry problems.



About the speaker
Prof. Vladimir Gavrilovich Romanov is a full member of Russian Academy of Sciences, and the head of a laboratory of the Sobolev Institute of Mathematics. He graduated from the Moscow State University in 1961. He received his Ph.D. in Mathematical Institute, Minsk in 1965. He became Doctor of Science in Institute of Mathematics, Novosibirsk in 1969. Prof. V.G. Romanov has published about 300 research papers and books. His research Interests include: differential and integral equations, ill-posed and inverse problems of mathematical physics, tomography applied mathematics, numerical analysis.