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A note concerning hyperbolic equations with constant coefficients

1960
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Quarterly of Applied Mathematics
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The canonical form of the linear, homogeneous hyperbolic partial differential equation in two independent variables is uxy + aux + buv + cu = 0, where a, b, c are functions of x, y. The constant coefficients case, frequently met in applitions, can be reduced to the simpler form vxu -\v = 0, X = ab -c with X constant, through the substitution v(x, y) -u exp (bx + ay). The solution of the Cauchy problem for an equivalent form of (2) with v and dv/dn prescribed along C is worked out explicitly by Copson [1] using the methods of M. Riesz. Fig. 1

doi:10.1090/qam/114044
fatcat:rq3jzetlineqhp4kzqd2yxtc4a