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.
$L^1-$Theory for Incompressible Limit of Reaction-Diffusion Porous Medium Flow with Linear Drift
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.AP 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
On the incompressible limit of Keller-Segel system with volume-filling effects
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.