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

Published online by Cambridge University Press:  20 November 2018

M. H. Protter
M. H. Protter*
Affiliation:
University of California at Berkeley
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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) = 0

with 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 542 - 553
Copyright
Copyright © Canadian Mathematical Society 1954

References

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