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The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cellpopulation models to free boundary problems of Hele–Shaw type. Although a vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV-uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces.
@article{AIHPC_2023__40_3_511_0,
author = {David, Noemi and D\k{e}biec, Tomasz and Perthame, Beno{\^\i}t},
title = {Convergence rate for the incompressible limit of nonlinear diffusion{\textendash}advection equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {511--529},
volume = {40},
number = {3},
year = {2023},
doi = {10.4171/aihpc/53},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/53/}
}
TY - JOUR AU - David, Noemi AU - Dębiec, Tomasz AU - Perthame, Benoît TI - Convergence rate for the incompressible limit of nonlinear diffusion–advection equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2023 SP - 511 EP - 529 VL - 40 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/53/ DO - 10.4171/aihpc/53 LA - en ID - AIHPC_2023__40_3_511_0 ER -
%0 Journal Article %A David, Noemi %A Dębiec, Tomasz %A Perthame, Benoît %T Convergence rate for the incompressible limit of nonlinear diffusion–advection equations %J Annales de l'I.H.P. Analyse non linéaire %D 2023 %P 511-529 %V 40 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/53/ %R 10.4171/aihpc/53 %G en %F AIHPC_2023__40_3_511_0
David, Noemi; Dębiec, Tomasz; Perthame, Benoît. Convergence rate for the incompressible limit of nonlinear diffusion–advection equations. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 3, pp. 511-529. doi: 10.4171/aihpc/53
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