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

## TL;DR

This paper proves short-time existence and uniqueness of solutions for a nonlinear moving boundary problem modeling evaporation in porous media, using advanced regularity results in an $L_{p}$ framework.

## Contribution

It introduces a novel proof of well-posedness for a complex two-phase elliptic-parabolic model with dynamic boundary conditions.

## Key findings

- Established short-time existence and uniqueness of solutions
- Developed nonstandard regularity results for elliptic-parabolic systems
- Validated the mathematical model for evaporation fronts in porous media

## 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.