Related papers: Boundary shape reconstruction with Robin condition…
In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two…
In this paper, we are interested to an inverse Cauchy problem governed by the Stokes equation, called the data completion problem. It consists in determining the unspecified fluid velocity, or one of its components over a part of its…
Following recent interest in the qualitative analysis of some optimal control and shape optimisation problems, we provide in this article a detailed study of the optimisation of Robin boundary conditions in PDE constrained calculus of…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
We study the boundary rigidity problem with partial data consisting of determining locally the Riemannian metric of a Riemannian manifold with boundary from the distance function measured at pairs of points near a fixed point on the…
We consider the reconstruction of a heterogeneous coefficient field in a Robin boundary condition on an inaccessible part of the boundary in a Poisson problem with an uncertain (or unknown) inhomogeneous conductivity field in the interior…
We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…
A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
The purpose of this study is twofold. First, we revisit a shape optimization reformulation of a prototypical shape inverse problem and briefly propose a simple yet efficient numerical approach for solving the corresponding minimization…
In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only the Dirichlet datum is known on the boundary that is to be…
We consider a non-autonomous Cauchy problem involving linear operators associated with time-dependent forms $a(t;.,.):V\times V\to {\mathbb{C}}$ where $V$ and $H$ are Hilbert spaces such that $V$ is continuously embedded in $H$. We prove…
We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…
We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…
This work is devoted to the nonlinear inverse problem of identifying the reaction coefficient in an elliptic boundary value problem from single Cauchy data on a part of the boundary. We then examine simultaneously two elliptic boundary…
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation…
We introduce Robin boundary conditions for biharmonic operators, which are a model for elastically supported plates and are closely related to the study of spaces of traces of Sobolev functions. We study the dependence of the operator, its…
We study some properties of Laplacian eigenvalues with negative Robin boundary conditions. We will show some monotonicity properties on annuli of the first eigenvalue by means of shape optimization techniques.