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Continuous data dependence for the equations of classical elastodynamics†

Published online by Cambridge University Press:  24 October 2008

R. J. Knops  and
L. E. Payne
R. J. Knops
Affiliation:
University of Newcastle; Cornell University
L. E. Payne
Affiliation:
University of Newcastle; Cornell University
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Extract

Consider a linear elastic solid occupying a bounded regular three-dimensional region B with smooth surface ∂B. The components of displacement ui referred to cartesian axes xi are then well known to satisfy the system of governing equations

in which t denotes the time variable, x = (x1, x2, x3) denotes the position vector, ρ(x) is the non-homogeneous density, assumed positive,. i(x, t) are the Cartesian components of body force per unit mass, and cijkl(x) are the non-homogeneous elasticities, which apart from certain smoothness conditions stated later, are assumed to possess the symmetry

Throughout this paper, all suffixes range over the values 1, 2, 3 and the usual converition of summing over repeated indices is adopted. Except where it is in the interest of clarity we avoid explicit mention of the dependence of functions on their arguments.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 481 - 491
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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