ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
In this paper we show the existence of periodic solutions for a class of non-linear regular vector fields of ∝3 admitting the trivial solution and depending on a real parameter μ. Two main assumptions lead to this conclusion: first, the right hand-side of each vector field anticommutes with a reflection. Then, its linear part admits the eigenvalue zero for all variations of μ, and takes the form of a three-dimensional Jordan block at μ = 0. This result allows the description of the bidimensional stationary patterns induced by a uniform heat-flux imposed on the boundaries of an infinite porous layer, saturated by a fluid. Indeed, when the filtration Rayleigh number comes close to its critical value, the field of seepage velocity and the field of temperature can be related to a partial differential equation, which admits a three-dimensional centre manifold. The existence of convective patterns follows. Their length depends on the filtration Rayleigh number, and tends towards infinity when this parameter comes close to its critical value (from above).
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670181403
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