Smoothness of Strong Solutions of Complete Hyperbolic Second-Order Differential Equations with Variable Domains of Operator Coefficients

Abstract

Smoothness properties of strong solutions of hyperbolic second-order differential equations with variable domains of operator coefficients in the case of a two-term leading part were analyzed in the paper [1, 2]. The paper [3] deals with the correct solvability of hyperbolic second-order operatordifferential equations with variable domains and with a three-term leading part. In the present paper, we consider smoothness properties of strong solutions of hyperbolic second-order operatordifferential equations with variable domains in the case of a three-term leading part. Boundary value problems for singular hyperbolic partial differential equations are examples of such operatordifferential equations [3].