Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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?)

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  • [2] L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. MR 0213845
  • [3] J. Kevorkian and Julian D. Cole, Perturbation methods in applied mathematics, Applied Mathematical Sciences, vol. 34, Springer-Verlag, New York-Berlin, 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] Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. 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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