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 Lp-setting. It relies critically on nonstandard optimal regularity results for a linear elliptic–parabolic system with dynamic boundary condition.

Original languageEnglish
Article number40
Number of pages31
JournalJournal of Mathematical Fluid Mechanics
Volume21
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

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

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