Asymptotics of the solution of a mixed problem for a system of differential equations connected with a positive integral operator

A mixed problem is considered for a hyperbolic system of partial differential equations for whose solutions there exist integral representations having a probability-theoretical meaning. It is assumed that the right-hand sides of the system satisfy exponential estimates. Under natural restrictions on the coefficients, the asymptotics of the solutions as $t\to\infty$ are obtained with the help of the theory of linear integral operators with nonnegative kernels, and the theory of branching processes with several types of particles in motion along an interval.
Bibliography: 10 titles.