Related papers: Carleman estimates for global uniqueness, stabilit…

In this paper, we establish a weight identity for stochastic beam equation by means of the multiplier method. Based on this identity, we first establish the global Carleman estimate for the special system with zero initial value and end…

In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions of parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator…

In this article, we improve the classical Bukhgeim-Klibanov method presented in [1],which can be used to prove the conditional stability of inverse source problem for a hyperbolic equation from the measurement on the subboundary. A major…

We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on controllability results through Carleman estimates for the associated adjoint problem. The novelty of the present paper is that the…

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

We consider a fractional radiative transport equation, where the time derivative is of half order in the Caputo sense. By establishing Carleman estimates, we prove the global Lipschitz stability in determining the coefficients of the…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to…

Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential…

We propose a global convergent numerical method to reconstruct the initial condition of a nonlinear parabolic equation from the measurement of both Dirichlet and Neumann data on the boundary of a bounded domain. The first step in our method…

In this paper, we study an inverse coefficients problem for two coupled Schr\"{o}dinger equations with an observation of one component of the solution. The observation is done in a nonempty open subset of the domain where the equations…

An approximately globally convergent numerical method for a 3d Coefficient Inverse Problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented. An approximation is used only on…

We propose a class of robust estimates for multivariate linear models. Based on the approach of MM estimation (Yohai 1987), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have…

In this paper, we obtain a Carleman estimate for the higher order partial differential operator. In the process of establishing this estimate, we developed a new method, which is called the back-propagation method (the BPM, for short). This…

In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…

My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics,…