Related papers: Inverse problems for the stationary transport equa…
We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
In this work, we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit, i.e. the normalized mean free path (the Knudsen number) $0 < \eps \ll 1$. It is…
We revisit the instability properties of the recovery of the absorption coefficient for the radiative transfer equation in the diffusive regime. To this end, we develop a rather robust framework building on [Koch-R\"uland-Salo, 2021] which…
This work considers a nonlinear inverse source problem in a coupled diffusion equation from the terminal observation. Theoretically, under some conditions on problem data, we build the uniqueness theorem for this inverse problem and show…
In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…
In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…
We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…
We consider inverse problems for the first and half order time fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates.
We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that,…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…
In this paper, we study the phenomenon of increasing stability in the inverse boundary value problems for the biharmonic equation. By considering a linearized form, we obtain an increasing Lipschitz-like stability when k is large.…
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…