TWO-DIMENSIONAL INVERSE PROBLEM FOR THE THERMOELASTICITY EQUATION OF MEMORY TYPE

A two-dimensional inverse problem of determining the kernel of the thermoelasticity equation of memory type is studied. It is assumed that the coefficients of the equations depend on only one spatial variable. Applying the linearization principle, the inverse problem is reduced to an equivalent linear system of integral equations. The generalized principle of contracted maps is applied to the latter in the space of continuous functions. The theorem of unique solvability is proved, and an estimate of the stability of the solution of the inverse problem is obtained.