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.

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  • [1] H. R. Pitt, Tauberian theorems, Tata Institute of Fundamental Research, Monographs on Mathematics and Physics, vol. 2, Oxford University Press, London, 1958. MR 0106376
  • [2] Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142
  • [3] José Néstor Distéfano, Sulla stabilità in regime viscoelastico a comportamento lineare. I, II, Atti. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 27 (1959), 205–211, 356–361 (Italian). MR 0116634
  • [4] J. N. Distéfano, Ancora sulla stabilità asintotica delle deflezioni di una trave viscoelastica, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 35 (1963), 504–508 (Italian). MR 0167046
  • [5] Vito Volterra, Theory of functionals and of integral and integro-differential equations, With a preface by G. C. Evans, a biography of Vito Volterra and a bibliography of his published works by E. Whittaker, Dover Publications, Inc., New York, 1959. MR 0100765
  • [6] V. Volterra and J. Pérès, Théorie Générale des Fonctionnelles, Gauthier-Villars, Paris, 1936
  • [7] F. G. Tricomi, Integral equations, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 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, 2nd ed, Dover Publications, 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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