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An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the…
We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, treated as an unknown Neumann boundary condition. Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data Assimilation…
Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…
In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the…
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…
We consider the inverse elastic scattering problems using the far field data due to one incident plane wave. A simple method is proposed to reconstruct the location and size of the obstacle using different components of the far field…
We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calder\'on's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic conductivity of a material filling a smooth bounded domain…
An inverse boundary value problem for the Helmholtz equation in a bounded domain is considered. The problem is to extract information about an unknown obstacle embedded in the domain with unknown impedance boundary condition (the Robin…
In this paper, we give probabilistic interpretations of both, the forward and the inverse problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities: Using the theory of symmetric Dirichlet…
This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and…
The enclosure method was originally introduced for inverse problems of concerning non-destructive evaluation governed by elliptic equations. It was developed as one of useful approaches in inverse problems and applied for various equations.…
The Dirichlet-to-Neumann map associated to an elliptic partial differential equation becomes multivalued when the underlying Dirichlet problem is not uniquely solvable. The main objective of this paper is to present a systematic study of…
We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…