L¹-Theory for Incompressible Limit of Reaction-Diffusion Porous\n Medium Flow with Linear Drift

2021/12/20 by Noureddine Igbida, Igbida, Noureddine
Computer Science · Engineering · Mathematics · #35A01 #35A02 #35B20 #35B35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.10411

openalex publication_date 2021/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our aim is to study the limit of the solution of reaction-diffusion porous\nmedium equation with linear drift ∂_t u -\Δ u^m\n+\∇ \⋅ (u : V)=g(t,x,u) , as m\→\∞. We study the problem in\nbounded domain \Ω with Dirichlet boundary condition, compatible initial\ndata ; i.e. vert u₀ vert \≤ 1, and an outpointing vector field V on the\nboundary \∂ \Ω. In particular, by means of new BV_loc\nestimates, we show uniform L¹-convergence towards the solution of\nreaction-diffusion Hele-Shaw flow with linear drift.\n

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