The qualitative analysis of a dynamical system of differential equations arising from the study of multilayer scales on pure metals II
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- by R. L. Baker PDF
- Proc. Amer. Math. Soc. 127 (1999), 753-761 Request permission
Abstract:
We provide a qualitative analysis of the $n$-dimensional dynamical system: \[ \dot q_i=-\sum _{j=1}^n \frac {a_{ij}}{q_j^k},\quad q_i(t)>0,\qquad i=1,\dots , n, \] where $k$ is an arbitrary positive integer. Under mild algebraic conditions on the constant matrix $A=(a_{ij})$, we show that every solution $\mathbf q(t)$, $t\in [0,a)$, extends to a solution on $[0,+\infty )$, such that $\lim _{t\to +\infty } q_i(t)=+\infty$, for $i=1,\dots , n$. Moreover, the difference between any two solutions approaches $0$ as $t\to +\infty$. 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.References
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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
- Received by editor(s): June 20, 1994
- Received by editor(s) in revised form: June 16, 1997
- Communicated by: David Sharp
- © Copyright 1999 American Mathematical Society
- 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