Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

On asymptotic stability of nonlinear hereditary phenomena


Authors: J. N. Distéfano and J. L. Sackman
Journal: Quart. Appl. Math. 24 (1966), 133-141
MSC: Primary 73.41
DOI: https://doi.org/10.1090/qam/202372
MathSciNet review: 202372
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Abstract: Conditions for long-term stability of nonlinear hereditary phenomena are derived from two Tauberian theorems. When the hereditary phenomena are time invariable (i.e., of the closed cycle type), then the asymptotic limits of the phenomena are evaluated. An application is made to the investigation of the stability of a rigid column restrained by a nonlinear viscoelastic element.


References [Enhancements On Off] (What's this?)

  • [1] H. R. Pitts, Tauberian Theorems, Oxford University Press, 1958 MR 0106376
  • [2] R. Paley and N. Wiener, Fourier Transforms in the Complex Domain, American Mathematical Society Colloquium Publications, 19 (1934) 59-63 MR 1451142
  • [3] J. N. Distefano, Sulla Stabilita in Regime Viscoelatica Comportamento Lineare, Rend. Acc. Naz. Lincei, fasc. 5, serie VIII, 27. (1959) and fasc. 6, serie VIII, 27 (1959) MR 0116634
  • [4] J. N. Distefano, Ancora Sulla Stabilita Asintotica delle Deflezioni de una Trave Viscoelastica, Rend. Acc. Naz. Lincei, fasc. 6, serie VIII, 35 (1963) MR 0167046
  • [5] V. Volterra, Theory of Functionals and of Integral and Integro-Differential Equations, Dover Pub., Inc., New York, 1959 MR 0100765
  • [6] V. Volterra and J. Pérès, Théorie Générale des Fonctionnelles, Gauthier-Villars, Paris, 1936
  • [7] F. Tricomi, Integral Equations, Interscience, New York, 1957 MR 0094665
  • [8] V. Volterra, Leçons sur les Fonctions des Lignes, Gauthier-Villars, Paris, 1913
  • [9] F. R. Shanley, Weight-Strength Analysis of Aircraft Structures, Second Ed., Dover Pub., Inc., New York, 1960 MR 0116580

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DOI: https://doi.org/10.1090/qam/202372
Article copyright: © Copyright 1966 American Mathematical Society

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