Geodesic
On behavior of the solution of a generalized Cauchy problem for the wave equation at infinity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 33-38

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We prove an asymptotic formula for a Cauchy problem for the wave equation for a point $(x,t)$ moving to infinity in a characteristic direction. Initial data are generalized functions with a compact support. 
@article{ZNSL_2002_285_a2,
     author = {A. S. Blagoveshchenskii and A. A. Novitskaya},
     title = {On behavior of the solution of a generalized {Cauchy} problem for the wave equation at infinity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--38},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a2/}
}
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A. S. Blagoveshchenskii; A. A. Novitskaya. On behavior of the solution of a generalized Cauchy problem for the wave equation at infinity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 33-38. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a2/