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

2017/02/15 by Friedrich Lippoth, Lippoth, Friedrich, Georg Prokert +1
Mathematics · #35M33 #35R37 (Primary) #76T10 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35M33 #msc:35R37 #msc:76T10

paper · pdf · doi:10.48550/arxiv.1702.04530

arxiv created 2017/02/15 · arxiv updated 2017/02/16

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.

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