Volume 8, Issue 5

- In this paper we deal with the inverse problem of determining cracks in an electrical conductor by finitely many boundary masurements of voltages and current. We prove uniqueness results for multiple cracks, possibly emerging on the surface of the conductor.

- In this paper we consider a two-surface problem for a biharmonic equation and formulate a sufficient condition for unique solvability of this problem and the conjugate problem in the class C 2 (D̅ 1 ) ∩ C 4 (D̅ 1 ).

- This paper is concerned with a quantitative nondestructive evaluation of conductors using superconducting quantum interference devices (SQUIDs). A measurement system is described for an electrical potential problem with an unknown boundary. Domain identification is discussed within the theoretical framework of parameter estimation problem for the electrostatic field analysis. Applying the method of mappings to the problem considered here, we present computational methods, including theoretical convergence results for the associated finite dimensional problem identification techniques.

- In this paper we prove a (local in time) existence and uniqueness theorem for the identification of a memory kernel h entering a parabolic integrodifferential equation with non commuting operators, related to a convex cylindrical domain, when the coefficient h is assumed to depend on time and one space variable.

- A variational approach is presented for numerical identification of the boundary conditions in solution of the Cauchy problem governed by the Navier equations in two-dimensional elasticity. The Cauchy problem in elastostatics is featured by simultaneously prescribed displacement and traction on a part of the boundary of an elastic body. The boundary data may contain some noise. The problem can be reformulated as a minimization problem of a functional with constraints, then the minimization problem is recast into successive primary and adjoint boundary value problems with no constraints in the corresponding plane elasticity problem. Two variational formulations, i. e., displacement approach and traction approach, are described. For an approximate solution of the elasticity problems, the conventional direct boundary element method is applied. Through simple examples, it is shown that our variational approaches are convergent and the proposed numerical process is stable.

- A mammography inverse problem for the diffusion equation in the frequency domain is considered. The extrapolated boundary condition is used in which the fluence is set to zero at an extrapolated boundary located a small distant away from (outside) the surface of the compressed breast. Uniqueness theorem is given for the linearized inverse problem of determining the diffusion and absorption coefficients from the reflection or transmission data at a single (non-zero) frequency.

- It is well known that for uniqueness of the exterior problem for the Radon transform it is necessary and sufficient that a function decays rapidly towards infinity. This is Helgason’s support theorem. Several years ago, J. Boman discussed a modification of this theorem by restricting the condition of rapid decay to an open cone. In this paper, we study this modification.