The Cauchy Problem for a Hyperbolic Second Order Equation with Data on the Parabolic Line

Abstract

In this paper we consider the Cauchy problem for the equation(1) h(x, y) K(y) vxx − vyy + a(x, y) vx + b(x, y) vy + c(x, y) v + f(x, y) = 0with initial values prescribed on a segment of the x-axis. The coefficients in (1) are assumed to possess two continuous derivatives with respect to x and one continuous derivative with respect to y in the closure of the domain under consideration.