The multidimensional problem of determining the density function for the system of viscoelasticity

摘要

We consider the problem of finding the thermal expansioncoefficient (z); z 2 [0;Z]; occurring in the system of integro-differentialtermoviscoelasticity equations. The medium density and the Lame parametersare assumed to be function of one variable. The integrand h(t); t 2[0; T] is known. The inverse problem is replaced by the equivalent integralequation for unknown functions. The theorem of unique solvability isproved and the stability estimate of solving the inverse problem is obtained.