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We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
In this note we present a reconstructive algorithm for solving the cross-sectional pipe area from boundary measurements in a tree network with one inaccessbile end. This is equivalent to reconstructing the first order perturbation to a wave…
We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…
The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is…
We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch…
In this paper we develop numerical algorithm for solving inverse problem for the wave equation using Boundary Control method. The results of numerical experiments are represented.
We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform…
An inverse boundary value problem for a 1+1 dimensional wave equation with wave speed $c(x)$ is considered. We give a regularisation strategy for inverting the map $\mathcal A:c\mapsto \Lambda,$ where $\Lambda$ is the hyperbolic…
We revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspective, we introduce a gradient-weighted modification of the…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…
We study the inverse problem of recovering the spatial support of parameter variations in a system of partial differential equations (PDEs) from boundary measurements. A reconstruction method is developed based on the monotonicity…
Ensuring the stability of power systems is gaining more attraction today than ever before, due to the rapid growth of uncertainties in load and renewable energy penetration. Lately, wide area measurement system-based centralized controlling…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of…
This paper is concerned with the inverse problem of time-harmonic acoustic scattering by an unbounded, locally rough interface which is assumed to be a local perturbation of a plane. The purpose of this paper is to recover the local…
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
We consider the inverse boundary value problem of determining the Lam\'e moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…