Search results for "Integral Equation"

Iterative continuous maximum-likelihood reconstruction method

1992

Reconstruction from boundary measurements for less regular conductivities

2012

In this paper, following Nachman's idea and Haberman and Tataru's idea, we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz domain $\Omega$ from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$.

Hyers-Ulam Stability of a Nonlinear Volterra Integral Equation on Time Scales

2020

We study Hyers-Ulam stability of a nonlinear Volterra integral equation on unbounded time scales. Sufficient conditions are obtained based on the Banach fixed point theorem and Bielecki type norm.

The perturbation classes problem for closed operators

2017

We compare the perturbation classes for closed semi-Fredholm and Fredholm operators with dense domain acting between Banach spaces with the corresponding perturbation classes for bounded semi-Fredholm and Fredholm operators. We show that they coincide in some cases, but they are different in general. We describe several relevant examples and point out some open problems.

Application of the ADR method for the evaluation of the scattering matrix of an open ended coaxial

2007

The use of ADR method for locating poles near the real axis is proposed when the scattering matrix for an open ended coaxial is analysed radiating over a multilayer structure ended in a perfect electrical wall. So a better and faster integral evaluation is made once the subintegral function behaviour is known.

Boundary element solution for free edge stresses in composite laminates

1997

The edge-stress problem in multilayered composite laminates under uniform axial extension is analyzed through an alternative method based on a boundary integral formulation. The basic equations of the formulation are discussed and solved by the multiregion boundary element method. Generalized orthotropic elasticity analytic fundamental solutions are employed to establish the integral equations governing the problem. The formulation is absolutely general with regard to the laminate stacking sequence and the section geometry and it does not require any aprioristic assumption on the elastic response nature. This makes the formulation suitable for an investigation of the singular behavior of th…

On the translation of the three fundamental problems of elastic equilibrium of anisotropic bodies into systems of Fredholm first kind integral equati…

1972

Bending stress fields in composite laminate beams by a boundary integral formulation

1999

Abstract The elasticity of a composite laminate under bending loads is approached through a boundary integral formulation and solved by the boundary element method. The integral equations governing the behaviour of each layer within the laminate, are deduced using the reciprocity theorem. Exact analytical singular solutions of the generalized orthotropic elasticity, i.e. the fundamental solutions of the problem, are employed as the kernels of the integral equation. The formulation does not make any assumption as to the nature of the elastic response and it allows consideration of general section geometries and stacking sequences. The solution is obtained through the enforcement of the inter…

Damage Identification of Beams Using Static Test Data

2003

A damage identification procedure for beams under static loads is presented. Damage is modelled through a damage distribution function which determines a variation of the beam stiffness with respect to a reference condition. Using the concept of the equivalent superimposed deformation, the equations governing the static problem are recast in a Fredholm’s integral equation of the second kind in terms of bending moments. The solution of this equation is obtained through an iterative procedure as well as in closed form. The latter is explicitly dependent from the damage parameters, thus, it can be conveniently used to set-up a damage identification procedure. Some numerical results are present…

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.