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Pré-Publication, Document De Travail Année : 2023

L 1 -THEORY FOR HELE-SHAW FLOW WITH LINEAR DRIFT

Noureddine Igbida

Résumé

The main goal of this paper is to prove $L^1$-comparison and contraction principles for weak solutions of PDE system corresponding to a phase transition diffusion model ofHele-Shaw type with addition of a linear drift. The flow is considered with a source term and subject to mixed homogeneous boundary conditions : Dirichlet and Neumann. The PDE can be focused to model for instance biological applications including multi-species diffusion-aggregation models and pedestrian dynamics with congestion. Our approach combines DiPerna-Lions renormalization type with Kruzhkov device of doubling and de-doubling variables. The $L^1$-contraction principle allows afterwards to handle the problem in a general framework of nonlinear semigroup theory in $L^1,$ taking thus advantage of this strong theory to study existence, uniqueness, comparison of weak solutions, $L^1$-stability as well as many further questions.
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Dates et versions

hal-03175798 , version 1 (21-03-2021)
hal-03175798 , version 2 (22-04-2021)
hal-03175798 , version 3 (24-05-2021)
hal-03175798 , version 4 (24-03-2023)

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  • HAL Id : hal-03175798 , version 4

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Noureddine Igbida. L 1 -THEORY FOR HELE-SHAW FLOW WITH LINEAR DRIFT. 2023. ⟨hal-03175798v4⟩
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