no. 3
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
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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.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/53
Classification : 35K57, 35K65, 35Q92, 35B45
Keywords: incompressible limit, rate of convergence, Porous medium equation, free boundary, Hele–Shaw problem 
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     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},
     year = {2023},
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     number = {3},
     doi = {10.4171/aihpc/53},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/53/}
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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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