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Resume Depuis les travaux de Van Dyke, la formulation de la théorie de la couche limite comme solution d'un problème de perturbation est désormais classique. D'autre part les tendances asymptotiques apportent des informations souvent déterminantes dans la recherche de la solution. C'est pourquoi nous présentons quelques problèmes relevant soit d'une technique soit de l'autre. En premier...
Résumé Nous allons étudier le comportement, lorsque le paramètre ɛ tend vers 0, de la solution uɛ d'une inéquation variationnelle elliptique associée à un opérateur du type ɛA+B; l'opérateur A est elliptique du second ordre, l'opérateur B est du premier ordre, et les convexes que nous considérons sont du type {v; v ≥ ψ} ou {v; ψ1 ≤ v ≤ ψ2}. Nous allons montrer que, dans les bonscas, la limite de u...
(a) Boundary-layer phenomena, as defined in the present paper, offer a more interesting field for further mathematical study than has been widely recognised. Especially worthy of study are the partially-parabolic problems, with their mixture of elliptic and parabolic features. (b) Numerical methods are now available for solving all the various kinds of boundarylayer problem. (c) Stream-line...
The method of matched asymptotic expansions is used here to analyze atmospheric flow in the vicinity of the ground, induced by a temperature difference between the ground and the fluid and also by the presence of a basic non perturbed flow. This analysis allows to obtain in a rational manner : first, two asymptotic models for the free convection phenomenon in the atmosphere and secondly, two...
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