On fractional powers of a pair of matrices and a plate-beam problem |
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Authors: | Marié Grobbelaar Van Dalsen |
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Institution: | Department of Mathematics and Applied Mathematics , University of Pretoria , Pretoria, 0002, South Africa |
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Abstract: | In this paper we consider the transversal deflections of a dynamically-coupled Von Kármán system consisting of a plate which has a beam attached to its one edge. The problem is considered in the form of a non-linear evolution problem in a product space. We show the existence of a unique local solution by following a fractional powers approach to first construct a “weak” solution in a larger space. Regularity properties for this solution yield a unique local strong solution for the original boundary-value problem. This approach entails the introduction of fractional powers of a pair of matrices. |
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Keywords: | Fractional Powers empathy plate-beam Von Kármán system dynamic boundary condition |
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