Volume 8, Issue 4

- In this note we prove the theorem on conditional well-posedness of the Cauchy problem for a differential equation of order m with unbounded operator coefficients.

- First we give a formula (procedure) for the reconstruction of the support function for unknown inclusion by means of the Dirichlet to Neumann map. In the procedure we never make use of the unique continuation property or the Runge approximation property of the governing equation. Second we apply the method to a similar problem for the Helmholtz equation.

- Necessary and sufficient conditions are established for the identifiability, or non-identifiability, of coefficients, e. g. modulus of elasticity, moment of inertia, conductivity, etc., from prescribed deflection and load acting on a beam associated to the Euler -Bernoulli beam theory.

- The problems of dynamical reconstruction of unknown distributed and boundary controls acting upon nonlinear hyperbolic equations are discussed. Regularized algorithms which reconstruct unknown input during the evolution of the process are designed. These algorithms are stable with respect to informational noises and computational errors.

- An infinite plate consisting elastic isotropic layers of various thickness and elastic properties is considered. It is assumed that a point force is applied normally to a boundary of the plate. An inverse problem of finding parameters of the elastic plate is studied. Under some assumptions it is proved that the displacements vector measured on the boundary of the plate uniquely determines elasticity modules and density of layers as well as their thickness. A procedure of recovering parameters from the data is given.

- In this paper we consider the finite-dimensional approximations for L -regularized solutions in the Hilbert space [4]. Necessary and sufficient conditions on the independent disturbances of operators A and L which provide the convergence of finite-dimensional approximations are defined in Theorem 2 (the main statement of the paper). Obtained results essentially generalize results of [2, 3] and in the sequel can be used for development of finite-difference approximation methods for solving integrodifferential equations [2, 4].

- In this paper we research three inverse problems for multivelocity equation for particle transfer. In the domain where the integral density of the particle flow is measured the inverse problems are reduced to the Cauchy problem for an analytic function. This allows us to establish the uniqueness theorems and to obtain the formulas of Carleman type for solutions of inverse problems in the whole domain of particle transfer.