Pith. sign in

REVIEW 1 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2112.10411 v2 pith:OMLEMVLN submitted 2021-12-20 math.AP

Noureddine Igbida This is my paper · ORCID
classification math.AP
keywords driftlinearreaction-diffusionboundaryflowlimitmediumomega
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Our aim is to study the limit of the solution of reaction-diffusion porous medium equation with linear drift $\displaystyle\partial_t u -\Delta u^m +\nabla \cdot (u \: V)=g(t,x,u) $, as $m\to\infty.$ We study the problem in bounded domain $\Omega$ with Dirichlet boundary condition, compatible initial data ; i.e. $\vert u_0\vert \leq 1,$ and an outpointing vector field $V$ on the boundary $\partial \Omega.$ In particular, by means of new $BV_{loc}$ estimates, we show uniform $L^1-$convergence towards the solution of reaction-diffusion Hele-Shaw flow with linear drift.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the incompressible limit of Keller-Segel system with volume-filling effects

    math.AP 2024-12 conditional novelty 7.0 of 10

    For the volume-filling Keller-Segel system, the incompressible limit is a Hele-Shaw free-boundary problem for K>1 and a hyperbolic Keller-Segel system for K≤1.

Pith tools