Steady convection in porous media. III. The structure of the solutions
type: Item
instance of: scholarly article
title: Steady convection in porous media. III. The structure of the solutions
zbMATH Open document ID: 0579.76092
DOI: 10.1016/0020-7225(85)90007-2
author: Dan Polisevski
published in: International Journal of Engineering Science
publication date: 1985-01-01T00:00:00Z
review text: [For the former parts see the reviews above (Zbl 0579.76090 and Zbl 0579.76091).] In this work it is proved that the set of solutions is homeomorphic to a compact set of \({\mathbb{R}}^ m\) (m sufficiently large), emphasizing the leading part of the temperature for this problem. Also it is shown that for ''almost all'' data the set of solutions is finite, while the continuum of solutions (with respect to the Rayleigh number) is a one-dimensional manifold of class \(C^ 1\).
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76R99
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 3928616
zbMATH Keywords: general properties
zbMATH Keywords: generic properties
zbMATH Keywords: one-dimensional manifold
zbMATH Keywords: of solutions
zbMATH Keywords: compact set of solutions
zbMATH Keywords: continuum of solutions
MaRDI profile type: Publication
full work available at URL: 0020-7225(85)90007-2
OpenAlex ID: W2047161125
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description: scientific article; zbMATH DE number 3928616