相关论文: Lipschitz stability of an inverse conductivity pro…
We extend the results of a work by L. H\"ormander in 1990 concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a…
We are interested in the inverse problem of recovering a Robin coefficient defined on some non accessible part of the boundary from available data on another part of the boundary in the nonstationary Stokes system. We prove a Lipschitz…
This work is concerned with the Cauchy problem for a coupled Schr\"odinger-Benjamin-Ono system $$\left \{ \begin{array}{l} i\partial_tu+\partial_x^2u=\alpha uv,\qquad t\!\in\![-T,T], \ x\!\in\!\mathbb R,\\ \partial_tv+\nu\mathcal…
We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where…
This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
Calder\'on's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stability when restricted to finite-dimensional classes.…
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…
A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is…
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…
We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space $H^s$…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…
We study the inverse boundary value problems of determining a potential in the Helmholtz type equation for the perturbed biharmonic operator from the knowledge of the partial Cauchy data set. Our geometric setting is that of a domain whose…
We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity $k$. We first consider the transmission problem in $\mathbb{R}^d$ and characterize solvability of the problem in terms of the…
It was shown by Nachbin in 1950 that an $n$-dimensional normed space $X$ is injective or equivalently is an absolute 1-Lipschitz retract if and only if $X$ is linearly isometric to $l_\infty^n$ (i.e., $\mathbb{R}^n$ endowed with the…
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shr\"odinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…
We study the stability issue for the inverse problem of determining a coefficient appearing in a Schr\"odinger equation defined on an infinite cylindrical waveguide. More precisely, we prove the stable recovery of some general class of…