Geodesic
The Cauchy problem with modified initial data for the generalized Euler--Poisson--Darboux equation
Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 141-157

Voir la notice de l'article provenant de la source Math-Net.Ru

For the equation $$ \varphi(y-\tau(x))\frac{\partial^2u}{\partial x\partial y}+a(x,y)\frac{\partial u}{\partial x}+b(x,y)\frac{\partial u}{\partial y}+c(x,y)u=f(x,y), $$ where $\varphi(t)$ is an increasing function with $\varphi(0)=0$, consider the Cauchy problem in different formulations determined by specifying the initial data in various forms on the curve $y=\tau(x)$. It is proved that the problems considered are uniquely solvable. Bibliography: 12 titles. 
@article{SM_1984_48_1_a6,
     author = {F. T. Baranovskii},
     title = {The {Cauchy} problem with modified initial data for the generalized {Euler--Poisson--Darboux} equation},
     journal = {Sbornik. Mathematics},
     pages = {141--157},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_48_1_a6/}
}
TY  - JOUR
AU  - F. T. Baranovskii
TI  - The Cauchy problem with modified initial data for the generalized Euler--Poisson--Darboux equation
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 141
EP  - 157
VL  - 48
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1984_48_1_a6/
LA  - en
ID  - SM_1984_48_1_a6
ER  - 
%0 Journal Article
%A F. T. Baranovskii
%T The Cauchy problem with modified initial data for the generalized Euler--Poisson--Darboux equation
%J Sbornik. Mathematics
%D 1984
%P 141-157
%V 48
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1984_48_1_a6/
%G en
%F SM_1984_48_1_a6
F. T. Baranovskii. The Cauchy problem with modified initial data for the generalized Euler--Poisson--Darboux equation. Sbornik. Mathematics, Tome 48 (1984) no. 1, pp. 141-157. http://geodesic.mathdoc.fr/item/SM_1984_48_1_a6/