@article{SM_1977_31_3_a3,
author = {N. Kh. Ibragimov and E. V. Mamontov},
title = {On the {{\CYRS}auchy} problem for the equation $u_{tt}-u_{xx}-\sum_{i,j=1}^{n-1}a_{ij}(x-t)u_{y_iy_j}=0$},
journal = {Sbornik. Mathematics},
pages = {347--363},
year = {1977},
volume = {31},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1977_31_3_a3/}
}
TY - JOUR
AU - N. Kh. Ibragimov
AU - E. V. Mamontov
TI - On the Сauchy problem for the equation $u_{tt}-u_{xx}-\sum_{i,j=1}^{n-1}a_{ij}(x-t)u_{y_iy_j}=0$
JO - Sbornik. Mathematics
PY - 1977
SP - 347
EP - 363
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1977_31_3_a3/
LA - en
ID - SM_1977_31_3_a3
ER -
N. Kh. Ibragimov; E. V. Mamontov. On the Сauchy problem for the equation $u_{tt}-u_{xx}-\sum_{i,j=1}^{n-1}a_{ij}(x-t)u_{y_iy_j}=0$. Sbornik. Mathematics, Tome 31 (1977) no. 3, pp. 347-363. http://geodesic.mathdoc.fr/item/SM_1977_31_3_a3/
[1] O. Tedone, “Sull'integrazione dell'equazione $\frac{\partial^2\varphi}{\partial t^2}-\sum^m_{i=1}\frac{\partial^2\varphi}{\partial x_i^2}=0$”, Annali di Mat. (3), 1 (1898), 1–23 | Zbl
[2] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, 1923 | Zbl
[3] M. Matisson, “Le probleme de M. Hadamard relatif á la diffusion des ondes”, Acta Math., 71 (1939), 249–282 | DOI | MR
[4] K. L. Stellmacher, “Eine Klasse Huygensscher Differentialgleichungen und ihre Integration”, Math. Ann., 130:3 (1955), 219–233 | DOI | MR | Zbl
[5] Pe Günther, “Ein Beispiel einer nichttrivialen Huygensschen Differentialgleichung mit vier unabhängigen Variablen”, Arch. Rat. Mech. and Analysis, 18:2 (1965), 103–106 | MR | Zbl
[6] H. X. Ibragimov, E. V. Mamontov, “Sur le problème de J. Hadamard relatif á la diffusion des ondes”, S. R. Acad. Scient., Paris, 270 (1970), 456–458 | MR | Zbl
[7] H. X. Ibragimov, Gruppy Li v nekotorykh voprosakh matematicheskoi fiziki, NGU, Novosibirsk, 1972
[8] L. Schwartz, Théorie des distributions, t. I, II, Hermann, Paris, 1950–1951 | MR | Zbl
[9] G. N. Vatson, Teoriya besselevykh funktsii, t. 1, IL, M., 1949
[10] R. Kurant, Uravneniya s chastnymi proizvodnymi, Mir, M., 1964 | MR
[11] L. P. Eizenkhart, Rimanova geometriya, IL, M., 1948