The method of matching asymptotic expansions for the solution of a hyperbolic equation with a small parameter

The author considers an initial-boundary value problem for the hyperbolic equation
$$ \varepsilon^2(u_{tt}-u_{xx})+a(x,t)u_t=f(x,t) $$
in a rectangle (here $\varepsilon$ is a small parameter and $a(x,t)\geqslant a_0>0$). It is assumed that the initial and boundary values of the function $u_\varepsilon(x,t)$ coincide at the lower corners of the rectangle. A complete asymptotic expansion of the solution in powers of $\varepsilon$ is constructed everywhere in the rectangle.
Bibliography: 5 titles.