Related papers: On reconstruction of Lam\'e coefficients from part…

We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a…

This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or…

In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…

In this paper we show that the shear modulus $\mu$ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently of the unknown elasticity tensor.

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…

We consider the Cauchy problem for the nonlinear dynamical Lam\'e system with double wave speeds in a $d$-dimensional $(d=2,3)$ periodic domain. Moreover, the equations can be transformed into a linearly degenerate hyperbolic system. We…

This paper is concerned with an inverse boundary value problem for the Helmholtz equation over a bounded domain. The aim is to reconstruct two constant coefficients together with the location and shape of a Dirichlet polygonal obstacle from…

Transient Elastography enables detection and characterization of tissue abnormalities. In this paper we assume that the displacements are modeled by linear isotropic elasticity system and the tissue displacement has been obtained by the…

This paper is concerned with inverse source problems for the time-dependent Lam\'e system in an unbounded domain corresponding to the exterior of a bounded cavity or the full space $\R^3$. If the time and spatial variables of the source…

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…

In this paper we study the local behavior of a solution to the Lam\'e system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies…

The purpose of this paper is twofold. First, we use a classical method to establish Gaussian bounds of the fundamental matrix of a generalized parabolic Lam\'{e} system with only bounded and measurable coefficients. Second, we derive a…

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…

We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open…

We consider the Cauchy problem for the wave equation in $\Omega\times{\mathbb R}$ with data given on some part of the boundary $\partial\Omega\times{\mathbb R}$. We provide a reconstruction algorithm for this problem based on analytic…

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…

We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions $d\ge 4$, with emphasis on characteristic data. A useful tool is provided by the…

We prove the uniqueness for an inverse problem of determining a matrix coefficient $P(x)$ of a system of evolution equations $\sigma \ppp_t u = \ppp_x^2 u(t,x) - P(x) u(t,x)$ for $0<x<\ell$ and $0<t<T$, where $\ell>0$ and $T>0$ are…

We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…

We consider the inverse problem of the simultaneous identification of the coefficients $\sigma$ and $q$ of the equation div$(\sigma\nabla u) + qu=0$ from the knowledge of the complete Cauchy data pairs. We assume that $\sigma=\gamma A$…