scholarly journals Global stability for an inverse problem in soil–structure interaction

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150117 ◽  
Author(s):  
G. Alessandrini ◽  
A. Morassi ◽  
E. Rosset ◽  
S. Vessella
Keyword(s):  
Inverse Problem ◽  
Soil Structure ◽  
Stability Estimate ◽  
Unknown Coefficient ◽  
Thin Elastic Plate ◽  
Concentrated Force ◽  
Reaction Coefficient ◽  
Slab Foundation ◽  
Interior Points ◽  
Hölder Stability

We consider the inverse problem of determining the Winkler subgrade reaction coefficient of a slab foundation modelled as a thin elastic plate clamped at the boundary. The plate is loaded by a concentrated force and its transversal deflection is measured at the interior points. We prove a global Hölder stability estimate under (mild) regularity assumptions on the unknown coefficient.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

The problem of determining the one-dimensional kernel of viscoelasticity equation with a source of explosive type

2020 ◽  
Vol 28 (1) ◽  
pp. 43-52
Author(s):  
Durdimurod Kalandarovich Durdiev ◽  
Zhanna Dmitrievna Totieva
Keyword(s):  
Inverse Problem ◽  
Hyperbolic Equations ◽  
Stability Estimate ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Weighted Norms ◽  
The Stability ◽  
The One ◽  
Global Unique Solvability

AbstractThe integro-differential system of viscoelasticity equations with a source of explosive type is considered. It is assumed that the coefficients of the equations depend only on one spatial variable. The problem of determining the kernel included in the integral terms of the equations is studied. The solution of the problem is reduced to one inverse problem for scalar hyperbolic equations. This inverse problem is replaced by an equivalent system of integral equations for unknown functions. The principle of constricted mapping in the space of continuous functions with weighted norms to the latter is applied. The theorem of global unique solvability is proved and the stability estimate of solution to the inverse problem is obtained.

Stability estimate for an inverse problem of the convection-diffusion equation

2020 ◽  
Vol 28 (1) ◽  
pp. 71-92
Author(s):  
Mourad Bellassoued ◽  
Imen Rassas
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Scalar Potential ◽  
Stability Estimate ◽  
Inverse Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

scholarly journals Energy- and Regularity-Dependent Stability Estimates for Near-Field Inverse Scattering in Multidimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Isaev
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Uniform Norm ◽  
Stability Estimate ◽  
Stability Estimates ◽  
Logarithmic Stability

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimensiond≥3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimensiond=2is also given.

Identification of an unknown coefficient in KdV equation from final time measurement

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
Kumarasamy Sakthivel ◽  
Soundararajan Gnanavel ◽  
Alemdar Hasanov ◽  
Raju K. George
Keyword(s):  
Optimization Problem ◽  
Kdv Equation ◽  
Identification Problem ◽  
Stability Estimate ◽  
Unknown Coefficient ◽  
Final Time ◽  
Physical Systems ◽  
Control Framework ◽  
The Cost ◽  
Variable Topography

AbstractIn this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg–de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the unknown coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the coefficient is also discussed.

The Stress State in Inhomogeneous Elastic Beam at Combined Strength

2014 ◽  
Vol 501-504 ◽  
pp. 645-648 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Elena V. Barmenkova ◽  
Alena V. Matveeva
Keyword(s):  
Inverse Problem ◽  
Stress State ◽  
Modulus Of Elasticity ◽  
Elastic Beam ◽  
Bending Moment ◽  
Optimization Method ◽  
Theory Of Elasticity ◽  
Simultaneous Action ◽  
Concentrated Force ◽  
Inhomogeneous Bodies

In paper describes a method of optimization the stress state of an elastic beam, subjected to the simultaneous action of the central application of concentrated force and bending moment. Optimization method based on solving the inverse problem of the theory of elasticity of inhomogeneous bodies, the essence of which is to determine the law of changing the modulus of elasticity on the beams height for which stress state will be given.

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