UNIQUENESS AND STABILITY OF A SOLUTION TO AN INVERSE THERMOELASTICITY PROBLEM. 1. FORMULATION OF THE PROBLEM

The problem of identifi cation of functions of a system of one-dimensional equations of heat conduction and elastic waves has been considered. A condition for the uniqueness of a solution has been formulated. The instability of the solution to an inverse problem and of the problem of smoothing has been shown with the example of employment of the iterative-variational regularization method. A fi nite-diff erence scheme has been constructed for the equation of elastic waves in the presence of the dependence of its functions on temperature. A computational experiment has been conducted which confi rms the instability of the inverse problem. Conclusions have been drawn on the direction of development of the regularization method for partial diff erential equations
   
Author:  A. G. Vikulov
Keywords:  thermoelasticity, inverse problems, regularization, variational method, fi nite-diff erence method
Page:  918