Well-posedness for a moving boundary model of an evaporation front in a porous medium

Friedrich Lippoth; Georg Prokert

doi:10.1007/s00021-019-0438-1

Well-posedness for a moving boundary model of an evaporation front in a porous medium

Friedrich Lippoth (Corresponding author), Georg Prokert

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Abstract

We consider a two-phase elliptic–parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear evolution problem in an L^p-setting. It relies critically on nonstandard optimal regularity results for a linear elliptic–parabolic system with dynamic boundary condition.

Original language	English
Article number	40
Number of pages	31
Journal	Journal of Mathematical Fluid Mechanics
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s00021-019-0438-1
Publication status	Published - 1 Sept 2019

Keywords

Elliptic–parabolic system
Hele-Shaw problem
inhomogeneous symbol
moving boundary
parabolic evolution equation
Stefan problem

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10.1007/s00021-019-0438-1

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KW - Hele-Shaw problem

KW - inhomogeneous symbol

KW - moving boundary

KW - parabolic evolution equation

KW - Stefan problem

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Well-posedness for a moving boundary model of an evaporation front in a porous medium

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Keywords

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