• Corpus ID: 233481532

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

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