L1-Theory for Incompressible Limit of Reaction-Diffusion Porous Medium Flow with Linear Drift
Abstract
Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift ∂t u - um +∇ · (u \: V)=g(t,x,u) , as m∞. We study the problem in bounded domain with Dirichlet boundary condition, compatible initial data ; i.e. u0 ≤ 1, and an outpointing vector field V on the boundary ∂ . In particular, by means of new BVloc estimates, we show uniform L1-convergence towards the solution of reaction-diffusion Hele-Shaw flow with linear drift.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.