Related papers: Global stability for an inverse problem in soil-st…
We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic…
We prove a new global stability estimate for the Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain or, more precisely, the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
The interaction between the foundation structures and the soil has been developed for many engineering applications. For the determination of the stress in foundation structure it is needed to determine the influence of the stiffness of…
We prove new global H\"older-logarithmic stability estimates for the near-field inverse scattering problem in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently…
We prove a global H\"older stability estimate for a hybrid inverse problem combining microwave imaging and ultrasound. The principal features of this result are that we assume to have access to measurements associated to a single, arbitrary…
We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…
We present a combined analytical approach and numerical study on the stability of a ring bound to an annular elastic substrate, which contains a circular cavity. The system is loaded by depressurizing the inner cavity. The ring is modeled…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$,…
For an inverse coefficient problem of determining a state-varying factor in the corresponding Hamiltonian for a mean field game system, we prove the global Lipschitz stability by spatial data of one component and interior data in an…
We prove a global logarithmic stability estimate for the Gel'fand-Calderon inverse problem on a two-dimensional domain.
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.
We study some hybrid inverse problems associated to BVP's for Schr\"odinger and Helmholtz type equations. The inverse problems we consider consist in the determination of coefficients from the knowledge of internal energies. We establish…
We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…