Lamination Convex Hull of Stationary Incompressible Porous Media Equations

Lauri Hitruhin; Sauli Lindberg

doi:10.1137/20M134633X

Lamination Convex Hull of Stationary Incompressible Porous Media Equations

Lauri Hitruhin^*, Sauli Lindberg

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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Abstract

We compute the lamination convex hull of the stationary incompressible porous media (IPM) equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends only on height. We relate the results to the infinite time limit of non-stationary IPM.

Original language	English
Pages (from-to)	491-508
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	53
Issue number	1
DOIs	https://doi.org/10.1137/20M134633X
Publication status	Published - 2021
MoE publication type	A1 Journal article-refereed

Keywords

incompressible porous media equations
relaxation
lamination convex hull
FLOW

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QUAMAP: Quasiconformal Methods in Analysis and Applications
Astala, K., Prats Soler, M. & Lindberg, S.
27/08/2019 → 30/04/2021
Project: EU: ERC grants

Cite this

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title = "Lamination Convex Hull of Stationary Incompressible Porous Media Equations",

abstract = "We compute the lamination convex hull of the stationary incompressible porous media (IPM) equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends only on height. We relate the results to the infinite time limit of non-stationary IPM.",

keywords = "incompressible porous media equations, relaxation, lamination convex hull, FLOW",

author = "Lauri Hitruhin and Sauli Lindberg",

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N2 - We compute the lamination convex hull of the stationary incompressible porous media (IPM) equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends only on height. We relate the results to the infinite time limit of non-stationary IPM.

AB - We compute the lamination convex hull of the stationary incompressible porous media (IPM) equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends only on height. We relate the results to the infinite time limit of non-stationary IPM.

KW - incompressible porous media equations

KW - relaxation

KW - lamination convex hull

KW - FLOW

U2 - 10.1137/20M134633X

DO - 10.1137/20M134633X

M3 - Article

VL - 53

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EP - 508

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

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Lamination Convex Hull of Stationary Incompressible Porous Media Equations

Abstract

Keywords

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QUAMAP: Quasiconformal Methods in Analysis and Applications

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