# $L^1$-Theory for reaction-diffusion Hele-Shaw flow with linear drift

@inproceedings{Igbida2021L1TheoryFR, title={\$L^1\$-Theory for reaction-diffusion Hele-Shaw flow with linear drift}, author={Noureddine Igbida}, year={2021} }

Abstract. The main goal of this paper is to prove L-comparison and contraction principles for weak solutions (in the sense of distributions) of Hele-Shaw flow with a linear Drift. The flow is considered with a general reaction term including the Lipschitz continuous case, and subject to mixed homogeneous boundary conditions : Dirichlet and Neumann. Our approach combines DiPerna-Lions renormalization type with Kruzhkov device of doubling and de-doubling variables. The L-contraction principle…

## One Citation

$L^1-$Theory for Incompressible Limit of Reaction-Diffusion Porous Medium Flow with Linear Drift

- Mathematics
- 2021

Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift ∂tu−∆u +∇·(uV ) = g(t, x, u), as m→ ∞. We study the problem in bounded domain Ω with…

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