Summary
A bilinear divergence identity is obtained, which differs from the usualLagrange divergence identity employed byRiemann. In the case of two independent variables, this new identity is used to unify the treatment ofCauchy's problem for hyperbolic equations, the initial value problem for parabolic equations, and theDirichlet problem for elliptic equations.
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This research was supported in whole or in part by the United States Air Force under Contract No. AF18(600)-573 monitored by the Office of Scientific Research, Air Research and Development Command.
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Diaz, J.B., Martin, M.H. A generalization of Riemann's method for partial differential equations. Annali di Matematica 36, 335–359 (1954). https://doi.org/10.1007/BF02412845
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DOI: https://doi.org/10.1007/BF02412845