WELL-POSEDNESS OF A DIRICHLET PROBLEM FOR A HYPERBOLIC TYPE INTEGRO-DIFFERENTIAL EQUATION

Abstract

In the paper we consider a Dirichlet problem for an integro-differential equation with Volterra type integral term. Proving a priori estimates for the differential and integral parts, we provide negative norms’ a priori estimates for the operator of the problem. Based on the latest, we formulate theorems regarding the well-posedness of the formulated boundary value problem.