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: A quadratic evolution equation of the form \[ \dot u = Lu + \epsilon Qu\] 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.
- Viorel Barbu, Nonlinear semigroups and differential equations in Banach spaces, Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff International Publishing, Leiden, 1976. Translated from the Romanian. MR 0390843
- L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964. Translated from the Russian by D. E. Brown; Edited by A. P. Robertson. MR 0213845
- J. Kevorkian and Julian D. Cole, Perturbation methods in applied mathematics, Applied Mathematical Sciences, vol. 34, Springer-Verlag, New York-Berlin, 1981. MR 608029
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)
- Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
K. Yosida, Functional analysis, Springer-Verlag, Berlin and New York, 1971
V. Barbu, Nonlinear semigroups and differential equations in banach spaces, Noordhoff, Leyden, 1976
L. V. Kaantorovich and G. P. Akilov, Functional analysis in normed spaces, Pergamon Press, Macmillan, New York, 1964
J. Kevorkian and J. Cole, Perturbation methods in applied mathematics. Springer-Verlag, Berlin and New York, 1981
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)
A. H. Nayfeh, Perturbation methods, Wiley, New York, 1973
K. Yosida, Functional analysis, Springer-Verlag, Berlin and New York, 1971
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Article copyright:
© Copyright 1983
American Mathematical Society
