Geodesic
The method of matching asymptotic expansions for the solution of a hyperbolic equation with a small parameter
Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 541-550 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SM_1984_48_2_a16,
     author = {T. N. Nesterova},
     title = {The method of matching asymptotic expansions for the solution of a~hyperbolic equation with a~small parameter},
     journal = {Sbornik. Mathematics},
     pages = {541--550},
     year = {1984},
     volume = {48},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_2_a16/}
}
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T. N. Nesterova. The method of matching asymptotic expansions for the solution of a hyperbolic equation with a small parameter. Sbornik. Mathematics, Tome 48 (1984) no. 2, pp. 541-550. http://geodesic.mathdoc.fr/item/SM_1984_48_2_a16/