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Journals and Conferences
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, here we show that the ill-posedness decreases when we increase the wave number.
In this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary… (More)
We construct complex geometrical optics solutions for the isotropic elasticity system concentrated near spheres. We then use these special solutions, called complex spherical waves, to identify inclusions embedded in an isotropic, inhomogeneous, elastic background.
We develop a reconstruction algorithm to determine penetrable obstacles inside a domain in the plane from acoustic measurements made on the boundary. This algorithm uses complex geometrical optics solutions to the Helmholtz equation with polynomial-type phase functions.
We consider the reconstruction of obstacles inside a bounded domain filled with an incompressible fluid. Our method relies on special complex geometrical optics solutions for the stationary Stokes equation with a variable viscosity.
We study the inverse problem of determining an electrical inclusion from boundary measurements. We derive a stability estimate for the linearized map with explicit formulae on generic constants that shows that the problem becomes more ill-posed as the inclusion is farther from the boundary. We also show that this estimate is optimal.
In this paper we prove a Hölder and Lipschitz stability estimates of determining the residual stress by a single pair of observations from a part of the lateral boundary or from the whole boundary. These estimates imply first uniqueness results for determination of residual stress from few boundary measurements.
We survey some recent results on the reconstruction of discontinuities by boundary measurements for elasticity and related systems in two dimensions. Our main tool is a new type of complex geometrical optics solutions.
In this paper, we prove that the inverse problems for 2D elasticity and for the thin plate with boundary data (finite or full measurements) are equivalent. Having proved this equivalence, we can solve inverse problems for the plate equation with boundary data by solving the corresponding inverse problems for 2D elasticity, and vice versa. For example, we… (More)
This note proposes a novel algorithm for robust partial eigenvalue assignment (RPEVA) problem for a cubic matrix pencil arising from modeling of vibrating systems with aerodynamic effects. The RPEVA problem for a cubic pencil is the one of choosing suitable feedback matrices to reassign a few (say 3 ) unwanted eigenvalues while leaving the remaining large… (More)