The qualitative analysis of a dynamical system

of differential equations arising from the

study of multilayer scales on pure metals II

Author:
R. L. Baker

Journal:
Proc. Amer. Math. Soc. **127** (1999), 753-761

MSC (1991):
Primary 34C35, 70K05

DOI:
https://doi.org/10.1090/S0002-9939-99-04563-3

MathSciNet review:
1469394

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Abstract | References | Similar Articles | Additional Information

Abstract: We provide a qualitative analysis of the -dimensional dynamical system:

where is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix , we show that every solution , , extends to a solution on , such that , for . Moreover, the difference between any two solutions approaches as . We then use this result to give a complete qualitative analysis of a 3-dimensional dynamical system introduced by F. Gesmundo and F. Viani in modeling parabolic growth of three-oxide scales on pure metals.

**1.**H. Akuezue, R. Baker, and M. W. Hirsch,*The qualitative analysis of a dynamical system modeling the formation of multilayer scales on pure metals*, SIAM J. Math. Anal.**25**(1994), 1167-1175. MR**95a:34053****2.**F. Gesmundo and F. Viani,*The formation of multilayer scales in the parabolic oxidation of pure metals*, J. Corrosion Sci.**18**(1978), 217-230.**3.**M. W. Hirsch,*Systems of differential equations that are competitive or cooperative*II:*Convergence almost everywhere*, SIAM J. Math. Anal.**16**(1985), 423-429. MR**87a:58137****4.**Manfred Peschel and Werner Mende,*The Predator-Prey Model*, Springer-Verlag, Wien-New York, 1986. MR**87i:92056b****5.**J. Smillie,*Competitive and cooperative tridiagonal systems of differential equations*, SIAM J. Math. Anal.**5**(1984), 530-534. MR**85g:58054****6.**H. L. Smith,*Periodic tridiagonal competitive and cooperative systems*, SIAM J. Math. Anal. (to appear).

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Additional Information

**R. L. Baker**

Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Email:
baker@math.uiowa.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04563-3

Keywords:
Differential equations,
dynamical systems,
nonlinear dynamical systems,
cooperative dynamical systems

Received by editor(s):
June 20, 1994

Received by editor(s) in revised form:
June 16, 1997

Communicated by:
David Sharp

Article copyright:
© Copyright 1999
American Mathematical Society