Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Conservation laws in viscoelasticity

Authors: Giacomo Caviglia and Angelo Morro
Journal: Quart. Appl. Math. 48 (1990), 503-516
MSC: Primary 73F15; Secondary 49S05, 73B99
DOI: https://doi.org/10.1090/qam/1074965
MathSciNet review: MR1074965
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Abstract: The evolution equations of a linear viscoelastic solid are written in terms of the Laplace transform of the displacement field. A corresponding reformulation of the condition of vanishing divergence for vector fields is then proposed and, through a systematic procedure, an explicit representation for a very large family of such conserved vectors is derived. As an application it is shown how a suitable choice of the admissible parameters leads to specific conservation laws which involve spatial means of linear momentum, angular momentum, stress, and displacement, in terms of the known body force, and initial and boundary data. As a further application a Betti-type reciprocity relation is derived. The connection with Noether's approach to conservation laws is also discussed.

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DOI: https://doi.org/10.1090/qam/1074965
Article copyright: © Copyright 1990 American Mathematical Society

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