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Singular perturbation analysis of an integrodifferential equation modelling filament stretching

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Abstract

A formal asymptotic scheme is used to determine the leading order behavior of a certain singularly perturbed integrodifferential equation which models the process of stretching a polymer filament. The inner solution describes the process during a boundary layer in time which occurs at the onset of elastic recovery. The outer solution describes the long term behavior of the elastic recovery, and a bound on the ultimate recovery is determined.

Zusammenfassung

Ein formales asymptotisches Schema wird benutzt, um das Verhalten der Leitordnung einer gewissen singular gestörten Integro-Differentialgleichung, die als Modell für den Dehnungsprozeß einer Polymerfaser dient, zu bestimmen. Die innere Lösung beschreibt den Prozeß in einem zeitlichen Randgebiet, das am Anfang der elastischen Rückstellung auftritt. Die äußere Lösung beschreibt das Langzeitverhalten der elastischen Rückstellung, und eine Grenze für die endgültige Rückstellung wird bestimmt.

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References

  1. A. S. Lodge, J. B. McLeod and J. A. Nohel,A nonlinear singularly perturbed Volterra integrodifferential equation occurring in polymer rheology, Proc. Roy. Soc. Edinburgh80 A, 99–137 (1978).

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Authors and Affiliations

  1. Dept. of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, Illinois, USA

    J. S. Angell & W. E. Olmstead

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  1. J. S. Angell
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  2. W. E. Olmstead
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Angell, J.S., Olmstead, W.E. Singular perturbation analysis of an integrodifferential equation modelling filament stretching. Z. angew. Math. Phys. 36, 487–490 (1985). https://doi.org/10.1007/BF00944639

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  • DOI: https://doi.org/10.1007/BF00944639

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