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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {The {Cauchy} problem with modified initial data for the generalized {Euler{\textendash}Poisson{\textendash}Darboux} equation},
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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/

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