Solutions similaires pour un problème de couches limites en milieux poreux

Belhachmi, Zakaria; Brighi, Bernard; Taous, K.

doi:10.1016/s1620-7742(00)00044-1

Cited by 10 publications

(21 citation statements)

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“…The (see also [15], [21], [4] and [5]). On the other hand, the author notes that Mr J. Watson has given a simple proof that (1.1)-(1.2) has no solution for γ = 0 and m ≤ −1.…”

Section: Resultsmentioning

confidence: 99%

“…with the boundary conditions The first set of boundary conditions (1.2) with α = m+1 2 and β = m for m ∈ R corresponds to prescribed heat on the plate as in [4], [5], [12], [14], [16], [21] and [24]. The second set of boundary conditions (1.3) with α = m + 2 and β = 2m + 1 for m ∈ R is for the prescribed surface heat flux as done in [10] and [13].…”

Section: Introductionmentioning

confidence: 99%

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Recent Advances on Similarity Solutions Arising During Free Convection

Brighi¹,

Hoernel²

2005

Progress in Nonlinear Differential Equations and Their Applications

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This paper reviews results about free convection near a vertical flat plate embedded in some saturated porous medium. We focus on a third order autonomous differential equation that gives a special class of solutions called similarity solutions. Two cases are under consideration: in the first one we prescribe the temperature on the plate and in the second one we prescribe the heat flux on it. We will also see that the same equation appears in other industrial processes.

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“…The (see also [15], [21], [4] and [5]). On the other hand, the author notes that Mr J. Watson has given a simple proof that (1.1)-(1.2) has no solution for γ = 0 and m ≤ −1.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Recent Advances on Similarity Solutions Arising During Free Convection

Brighi¹,

Hoernel²

2005

Progress in Nonlinear Differential Equations and Their Applications

Self Cite

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“…For mathematical results about existence, nonexistence, uniqueness, nonuniqueness and asymptotic behavior, see [2], [5], [6] and [28] for γ = 0, and [9], [12], [15], [23] and [24] for the general case. Numerical investigations can be found in [2], [7], [16], [18], [28], [30] and [38].…”

Section: The Semi-infinite Vertical Flat Plate Casementioning

confidence: 99%

Steady Free Convection in a Bounded and Saturated Porous Medium

Akesbi¹,

Brighi²,

Hoernel³

2006

Recent Advances on Elliptic and Parabolic Issues

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In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the one of free convection near a semi-infinite impermeable vertical flat plate embedded in a fluid saturated porous medium. We establish the existence and uniqueness of the solution for small data in some unusual spaces.

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“…These boundary value problems have been widely studied, and mathematical results about them can be found, for example, in [1], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [17], [18], [20] and [21].…”

Section: Introductionmentioning

confidence: 99%

“…See [2] for details on the derivation of the problem (1)- (4). In the following, we will denote by (·, ·) the L 2 (Ω)-scalar product, and by · (resp.…”

Section: Introductionmentioning

confidence: 99%