Related papers: Inverse source problem and null controllability fo…

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability…

In this article, for a fourth-order parabolic equation which is closely related for example to the Cahn-Hilliard equation, we study an inverse source problem by interior data and the continuation of solution from lateral Cauchy data. Our…

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…

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…

This paper presents an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a…

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…

In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…

For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…

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…

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.

This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

In this paper, we investigate an inverse Cauchy problem for a stochastic hyperbolic equation. A Lipschitz type observability estimate is established using a pointwise Carleman identity. By minimizing the constructed Tikhonov-type…

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. As applications of these discrete Carleman estimates, we apply them to study two inverse problems…

We shall study in this paper the Lipschitz type stabilities and convergence rates of Tikhonov regularization for the recovery of the radiativities in elliptic and parabolic systems with Dirichlet boundary conditions. The Lipschitz type…

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…

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

In this article we establish the well-posedness, energy estimates, stability, and local null controllability for the thermistor system modeled by a parabolic-parabolic system using a control force acting on just one equation of the system.…