On a Penalty-Perturbation Theory for Plate Problems

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Abstract
A penalty-perturbation method previously proposed by Westbrook (J. Inst. Maths Applics (1974) 14, 79–82) for the solutions of static bending problems for elastic plates is analysed here. The method replaces the single fourth-order biharmonic equation by a system of three second-order equations which is “singularly” perturbed with respect to a small penalty parameter ε. The existence of solutions of the perturbed problem for each ε > 0 is established and the behaviour of these solutions as ε → 0 0 is studied. In particular, the results show that while these solutions are continuous in ε at ε = 0, analyticity in ε at ε = 0 is lost except in special cases.

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