Related papers: Global Lipschitz stability for an inverse source p…
We consider inverse problems of determining coefficients or time independent factors of source terms in radiative transport equations by means of Carleman estimate. We establish global Lipschitz stability results with an additional…
For linearized Navier-Stokes equations, we first derive a Carleman estimate with a regular weight function. Then we apply it to establish conditional stability for the lateral Cauchy problem and finally we prove conditional stability…
This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity…
For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an…
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
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.
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…
We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we…
We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…
In a bounded domain $\Omega \subset \mathbb{R}^d$ over time interval $(0,T)$, we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin…
We consider the Kelvin-Voigt model for the viscoelasticity, and prove a Carleman estimate for functions without compact supports. Then we apply the Carleman estimate to prove the Lipschitz stability in determining a spatial varying function…
This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…
We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove…
We consider the nonstationary linearized Navier-Stokes equations in a bounded domain and first we prove a Carleman estimate with a regular weight function. Second we apply the Carleman estimate to a lateral Cauchy problem for the…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…