Related papers: Stability estimate for the discrete Calderon probl…
In this paper, we describe a framework to compute expected convergence rates for residuals based on the Calder\'on identities for general second order differential operators for which fundamental solutions are known. The idea is that these…
In this work, we present some new Carleman inequalities for Stokes and Oseen equations with non-homogeneous boundary conditions. These estimates lead to log type stability inequalities for the problem of recovering the solution of the…
In this paper we improve an earlier result by Bukhgeim and Uhlmann, by showing that in dimension larger than or equal to three, the knowledge of the Cauchy data for the Schr\"odinger equation measured on possibly very small subsets of the…
We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the…
We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a…
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned problem by replacing integer derivatives with fractional…
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 is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the the unique continuation problem…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…
We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
Fully-discrete approximations of the Allen-Cahn equation are considered. In particular, we consider schemes of arbitrary order based on a discontinuous Galerkin (in time) approach combined with standard conforming finite elements (in…
In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…
In this paper we will review the main results concerning the issue of stability for the determination unknown boundary portion of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and selfcontained proofs.…
We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on…
We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…