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Improved estimates for continuous data dependence in linear elastodynamics

Published online by Cambridge University Press:  24 October 2008

R. J. Knops  and
L. E. Payne
R. J. Knops
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh
L. E. Payne
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York
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Extract

In a previous paper [6], the present authors established estimates for the continuous dependence of the solution on various data in the initial boundary value problem of linear elastodynamics on a bounded region of space. The main conclusion concerned continuous dependence on the body-force, but also it was shown how this result could be used to derive continuous dependence on the initial data, elasticities, boundary data and initial geometry. The method adopted was based upon logarithmic convexity arguments and hence led naturally to continuity in the sense of Hölder on compact sub-intervals of time. A special feature of the study entailed the lack of any sign-definiteness conditions on the elasticities which, of course, in the absence of any a priori constraint on the solution always gives rise to an ill-posed problem. (See, for instance, the comprehensive survey by Payne [10].)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 535 - 559
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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