Bifurcation with Memory
- 1 April 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 46 (2), 171-188
- https://doi.org/10.1137/0146013
Abstract
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time $\lambda $, controls the bifurcation behavior as the control parameter R is increased. Small (large) $\lambda $ gives steady (periodic) bifurcation. There is a double eigenvalue at $\lambda = \lambda _1 $, separating purely steady $(\lambda < \lambda _{1} )$ from combined steady/T-periodic $(\lambda > \lambda _{1} )$ states with $T \to \infty $ as $\lambda \to \lambda _1^ + $. Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from $\lambda = \lambda _1 $.
Keywords
This publication has 4 references indexed in Scilit:
- Nonlinear periodic convection in double-diffusive systemsJournal of Fluid Mechanics, 1981
- Nonlinear thermal convection in an elasticoviscous layer heated from belowProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1977
- Slow motion and viscometric motion; stability and bifurcation of the rest state of a simple fluidArchive for Rational Mechanics and Analysis, 1974
- Convective Stability of a General Viscoelastic Fluid Heated from BelowPhysics of Fluids, 1972