Summary
In [1] we reduced the solution of a classical boundary-value problem, namely the biharmonic equation in a rectangular domain, to a Cauchy formulation. The theory was developed in the context of elementary thin plate theory. It was shown that a rectangular plate with three edges clamped and the fourth edge free can be completely described by a system of integro-differential equations subject to initial values. In this paper we prove the converse, i.e., that any solution of the Cauchy system is a solution of the biharmonic equation, completing the equivalence.
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References
E. Angel, N. Distefano and A. Jain, Invariant Imbedding and the Reduction of Boundary-Value Problems of Thin Plate Theory to Cauchy Formulations,International Journal of Engineering Sciences, (In press).
R. Bellman and R. Kalaba, On the Fundamental Equations of Invariant Imbedding, I.Proc. National Academy of Science, U. S. 47 (1961) 336.
E. Angel and N. Distefano, Invariant Imbedding and the Effect of Changes of Poisson's Ratio in Thin Plate Theory,International Journal of Engineering Sciences, (In press).
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Angel, E., Distefano, N. Equivalence of a Cauchy system and a class of boundary-value problems in thin plate theory. J Eng Math 6, 117–123 (1972). https://doi.org/10.1007/BF01535095
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DOI: https://doi.org/10.1007/BF01535095