Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Asymptotic solutions of partial differential equations with damping and delay

Authors: G. N. Bojadziev and R. W. Lardner
Journal: Quart. Appl. Math. 33 (1975), 205-214
MSC: Primary 35R10; Secondary 35C99
DOI: https://doi.org/10.1090/qam/447854
MathSciNet review: 447854
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Abstract: Certain hyperbolic partial differential equations with small nonlinearities involving significant damping as well as time delay are investigated. The Krylov--Bogoliubov--Mitropolskii method is extended and applied. An application is given to longitudinal vibrations of a nonlinear elastic rod.

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

  • [1] Yu. A. Mitropolskii and B. I. Moseenkov, Lectures on the application of asymptotic methods to the solution of equations with partial derivatives (in Russian), Ac. of Sci. Ukr. SSR, Kiev, 1968
  • [2] V. I. Fodchuk, Application of the averaging method to the differential-difference equations of the neutral type, in Proceedings of the fourth conference on nonlinear oscillations, Prague (1968), 161-165
  • [3] G. N. Bojadziev and R. W. Lardner, Monofrequent oscillations in mechanical systems governed by second order hyperbolic differential equations with small non-linearities, Int. J. Non-Linear Mechanics 8, 289-302 (1973) MR 0334623
  • [4] Z. Osinski, Longitudinal, torsional and bending vibrations of a uniform bar with nonlinear internal friction and relaxation, in Nonlinear vibration problems, P. Ac. of Sci. Warsaw 4, 159-166 (1962)
  • [5] I. P. Popov and N. P. Paltov, Approximate methods for analyzing nonlinear automatic systems (in Russian), Gos. Izdat. Fiz.-Math. Lit., Moscow, 1960
  • [6] R. E. Bellman and K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963 MR 0146481

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DOI: https://doi.org/10.1090/qam/447854
Article copyright: © Copyright 1975 American Mathematical Society

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