The Cauchy problem with modified initial data for the generalized Euler–Poisson–Darboux equation

F. T. Baranovskii


Abstract: 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.

UDC: 517.946

MSC: Primary 35A05, 35L15, 35L80, 35Q05; Secondary 35M05, 35R25

Received: 24.07.1981

 English version: Mathematics of the USSR-Sbornik, 1984, 48:1, 141–157

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