Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Energy-like Liapunov functionals for linear elastic systems on a Hilbert space

Author: J. A. Walker
Journal: Quart. Appl. Math. 30 (1973), 465-480
MSC: Primary 34G05; Secondary 34D20
DOI: https://doi.org/10.1090/qam/508715
MathSciNet review: 508715
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Abstract: An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium; i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

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DOI: https://doi.org/10.1090/qam/508715
Article copyright: © Copyright 1973 American Mathematical Society

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