The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation

The problem of determining the kernel $h(t)$, $t\in[0,T]$, appearing in the system of integro-differential thermoviscoelasticity equations is considered. It is assumed that the coefficients of the equations depend only on one space variable. The inverse problem is replaced by the equivalent system of integral equations for unknown functions. The contraction mapping principle with weighted norms is applied to this system in the space of continuous functions. A global unique solvability theorem is proved and an estimate of the stability of the solution of the inverse problem is obtained.