An initial-boundary value problem for an equation of the mixed parabolic-hyperbolic type with distributed delay

Some problems [1-5] describing processes in media in which: in general, the state of the medium at given time depends on its states At all previous time moments lead to an integro-differential equation of the mixed parabolic-hyperbolic type with distributed delay (with memory). In the present paper! we consider a problem for a certain class of such equations, prove existence and uniqueness theorems. present an example of the solution of a particular equation, and estimate the solution under the unbounded growth of the time variable for parameter values related by specific conclusions.