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Article Dans Une Revue (Data Paper) Applied Mathematics Letters Année : 2024

A Nonlinear Elliptic Equation with a Degenerate Diffusion and a Source Term in L 1

Résumé

We study a simplified equation governing turbulent kinetic energy $k$ in a bounded domain, arising from turbulence modeling where the eddy diffusion is given by $\varrho(x) + \varepsilon$, with $\varrho$ representing the Prandtl mixing length of the order of the distance to the boundary, and a right-hand side in $L^1$. We obtain estimates of $\sqrt \varrho \g k$ in $L^q$ spaces and we establish the convergence toward the formal limit equation in the sense of the distributions as $\varepsilon$ goes to 0.
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Dates et versions

hal-04392244 , version 1 (13-01-2024)
hal-04392244 , version 2 (22-01-2024)

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  • HAL Id : hal-04392244 , version 2

Citer

Guillaume Leloup, Roger Lewandowski. A Nonlinear Elliptic Equation with a Degenerate Diffusion and a Source Term in L 1. Applied Mathematics Letters, 2024, 153, pp.109077. ⟨hal-04392244v2⟩
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