Stability estimates for the solution in the problem of determining the kernel of the viscoelasticity equation

For the integrodifferential equation of 2-dimensional viscoelasticity we study the problem of determining the spatial part of the kernel of the integral part of the equation on assuming that the unknown function is supported on some compact region $\Omega$. As data required for solving this inverse problem, on the boundary of $\Omega$ we specify the traces of the solution to the direct Cauchy problem and its normal derivative on some finite interval of time. A significant circumstance in the statement of this problem is that the solution to the direct Cauchy problem corresponds to zero initial data and time impulsive force localized on a fixed straight line disjoint from $\Omega$. The main result of this article is a Lipschitz estimate for the conditional stability of the solution to this inverse problem.