Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The generalized partial correspondence principle in linear viscoelasticity


Authors: G. A. C. Graham and J. M. Golden
Journal: Quart. Appl. Math. 46 (1988), 527-538
MSC: Primary 73F15
DOI: https://doi.org/10.1090/qam/963588
Erratum: Quart. Appl. Math. 49 (1991), 397.
MathSciNet review: 963588
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Abstract: A result, referred to as the generalized partial correspondence principle, is proved for noninertial viscoelastic boundary value problems. This states that if $ B_u^{\left( i \right)}\left( t \right)$, $ B_\sigma ^{\left( i \right)}\left( t \right)$ are the complementary regions of the boundary of a viscoelastic medium with a unique Poisson's ratio, on which displacements $ {u_i}\left( {r, t} \right)$ and stresses $ {\sigma _{ij}}\left( {r, t} \right){n_j}$ are specified, respectively, then if $ B_\sigma ^{\left( i \right)}\left( {t'} \right) \subseteq B_\sigma ^{\left( i \right)}\left( t \right)$ for all $ t' \le t$, the stresses satisfying this mixed boundary value problem at time $ t$ are the stresses for the elastic problem with the same boundary regions and the same specified stresses while known functions take the place of the specified displacements. It is noteworthy that $ B_\sigma ^{\left( i \right)}\left( {t'} \right)$, $ t' \le t$, is not required to be monotonic increasing.


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DOI: https://doi.org/10.1090/qam/963588
Article copyright: © Copyright 1988 American Mathematical Society


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