6 papers
Direct Sampling Methods for Inverse Interface Problems
Kazufumi Ito, Tong Wu, Jun Zou
This work investigates two types of inverse interface problems in scenarios where only very limited Cauchy data is available. These problems are associated with the Laplace equatio…
A Weighted Sampling Method for Inverse Medium Problem with Limited Aperture
Fuqun Han, Kazufumi Ito
Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constrai…
Iterative Direct Sampling Method for Elliptic Inverse Problems with Limited Cauchy Data
Kazufumi Ito, Bangti Jin, Fengru Wang +1
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the o…
Inverse medium problems, saddle point formulation
Kazufumi Ito
In this paper we discuss inverse medium problems. We develop the direct sampling method based on probing indices using the saddle point formulation. The medium is constructed by so…
Inverse coefficient problems for one-dimensional time-fractional diffusion equations
Oleg Imanuvilov, Kazufumi Ito, Masahiro Yamamoto
We prove the uniqueness in determining a spatially varying zeroth-order coefficient of a one-dimensional time-fractional diffusion equation by initial value and Cauchy data at one…
A Neumann interface optimal control problem with elliptic PDE constraints and its discretization and numerical analysis
Zhiyue Zhang, Kazufumi Ito, Zhilin Li
We study an optimal control problem governed by elliptic PDEs with interface, which the control acts on the interface. Due to the jump of the coefficient across the interface and t…