Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A perturbation method for solving a quadratic evolution equation

Authors: John W. Hilgers and Robert J. Spahn
Journal: Quart. Appl. Math. 41 (1983), 343-351
MSC: Primary 34G20; Secondary 34E05
DOI: https://doi.org/10.1090/qam/721425
MathSciNet review: 721425
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Abstract | References | Similar Articles | Additional Information

Abstract: A quadratic evolution equation of the form

$\displaystyle \dot u = Lu + \epsilon Qu$

is considered where $ L$ and $ Q$ are particular linear and quadratic integral operators respectively. This equation has been proposed to describe the variation with time of $ u(x,t)$, the volume density of an ensemble of particles undergoing concurrent coalescence and fracture.

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

  • [1] V. Barbu, Nonlinear semigroups and differential equations in banach spaces, Noordhoff, Leyden, 1976 MR 0390843
  • [2] L. V. Kaantorovich and G. P. Akilov, Functional analysis in normed spaces, Pergamon Press, Macmillan, New York, 1964 MR 0213845
  • [3] J. Kevorkian and J. Cole, Perturbation methods in applied mathematics. Springer-Verlag, Berlin and New York, 1981 MR 608029
  • [4] K. L. Kuttler, J. W. Hilgers and T. H. Courtney, An evolution equation for the volume distribution of particles undergoing mechanical or chemical interaction (in preparation)
  • [5] A. H. Nayfeh, Perturbation methods, Wiley, New York, 1973 MR 0404788
  • [6] K. Yosida, Functional analysis, Springer-Verlag, Berlin and New York, 1971

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Additional Information

DOI: https://doi.org/10.1090/qam/721425
Article copyright: © Copyright 1983 American Mathematical Society

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