1,721,009 research outputs found
Stable determination of the surface impedance of an obstacle by far field measurements
No full textWe 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
Stability and reconstruction for inverse corrosion problems
No full textWe collect some stability and reconstruction results for two inverse boundary value problems
arising in corrosion detectio
Smoothness dependent stability in corrosion detection
No full textWe consider the stability issue for the determination of a linear corrosion in a conductor by a single electrostatic measurement. We established a global log–log type stability when the corroded boundary is simply Lipschitz. We also improve such a result obtaining a global log stability by assuming that the damaged boundary is C1,1-smooth
Stability for the determination of unknown boundary and impedance with a Robin boundary condition
No full textWe consider an inverse problem arising in corrosion detection. We prove a stability
result of logarithmic type for the determination of the corroded portion of the boundary and
impedance by two measurements on the accessible portion of the boundary
Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary
Full text linkThe main result of the present paper consists in a quanti- tative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let u be a solution to the wave equation that satisfies an homogeneous Robin condition on a portion S of the boundary and the restriction of u on S is flat on a segment \{0\} \times J with 0 \in S then u|S vanishes in a neighbourhood of \{0\} \times J
Non-Singular Method of Fundamental Solutions based on Laplace decomposition for 2D Stokes flow problems
No full textIn this paper, a solution of Two-Dimensional (2D) Stokes flow problem, subject to Dirichlet and fluid traction boundary conditions, is developed based on the Non-singular Method of Fundamental Solutions (NMFS). The Stokes equation is decomposed into three coupled Laplace equations for modified components of velocity, and pressure. The solution is based on the collocation of boundary conditions at the physical boundary by the fundamental solution of Laplace equation. The singularities are removed by smoothing them on disks around them. The derivatives on the boundary in the singular points are calculated through simple reference solutions. In NMFS, no artificial boundary is needed, as in the classical Method of Fundamental Solutions (MFS). Numerical examples include driven cavity flow on a square, analytically solvable solution on a circle and channel flow on a rectangle. The accuracy of the results is assessed by comparison with the MFS solution, and analytical solutions. The main advantage of the approach is its simple, boundary only meshless character of the computations, and possibility of straightforward extension of the approach to Three-Dimensional (3D) problems, moving boundary problems and inverse problems
Solving elliptic Cauchy problems and the identification of nonlinear corrosion
No full textWe deal with an inverse problem arising in corrosion detection. The presence of corrosion damage is modeled by a nonlinear boundary condition on the inaccessible portion of the metal specimen. We propose a method for the approximate reconstruction of such a nonlinearity. A crucial step of this procedure, which encapsulates the major cause of the ill-posedness of the problem, consists of the solution of a Cauchy problem for an elliptic equation. For this purpose we propose an SVD approach
Local stability for soft obstacles by a single measurement
No full textWe consider an inverse scattering problem arising in target iden-
tification. We prove a local stability result of logarithmic type for the deter-
mination of a sound soft obstacle from the far field measurements associated
to one single incident wave
Detecting nonlinear corrosion by electrostatic measurements
No full textWe deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one
Logarithmic convergence rates for the identification of a nonlinear Robin coefficient
No full textWe consider the identification of a nonlinear corrosion profile from single voltage boundary
data and show injectivity of the parameter-to-output map. We demonstrate that Tikhonov
regularization can be applied in order to solve the inverse problem in a stable manner
despite the presence of noisy data. In combination with a logarithmic stability estimate
for the underlying Cauchy problem, rates for the convergence of the regularized solutions
are proven using a source condition that does not involve the Fréchet derivative of the
parameter-to-output map. We present sufficient conditions for the existence of a source
function and illustrate our approach by means of numerical example
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