Geodesic
On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 30 (1975) no. 2, pp. 1-58

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In this paper we study the Cauchy problem and boundary-value problem of general form in the exterior of a compact set for hyperbolic operators $L$, whose coefficients depend only on $x$ and are constant near infinity. Assuming that the wave fronts of the Green's matrix for $L$ go off to infinity as $t\to\infty$, we determine the asymptotic behaviour of solutions as $t\to\infty$. For the corresponding stationary problem we obtain the short-wave asymptotic behaviour of solutions for real and complex frequencies. 
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     author = {B. R. Vainberg},
     title = {On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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B. R. Vainberg. On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 30 (1975) no. 2, pp. 1-58. http://geodesic.mathdoc.fr/item/RM_1975_30_2_a0/