The problem of determining the one-dimensional kernel of the electroviscoelasticity equation

We consider the problem of finding the kernel $K(t)$, for $t\in[0,T]$, in the integrodifferential system of electroviscoelasticity. We assume that the coefficients depend only on one spatial variable. Replacing the inverse problem with an equivalent system of integral equations, we apply the contraction mapping principle in the space of continuous functions with weighted norms. We prove a global unique solvability theorem and obtain a stability estimate for the solution to the inverse problem.