Existence results for a biofilm free-boundary problem with dominant detachment

TL;DR

This paper proves the existence and uniqueness of solutions for a biofilm free-boundary problem with dominant detachment, extending prior models and providing insights into biofilm dynamics under specific conditions.

Contribution

It introduces new existence and uniqueness results for a biofilm free-boundary problem with dominant detachment, advancing mathematical understanding in this area.

Findings

Local existence and uniqueness established

Continuous dependence on initial data proven

Global existence deduced using invariance regions and energy estimates

Abstract

This work addresses the existence and uniqueness of a Wanner-Gujer free-boundary problem that models biofilms under conditions of prevailing detachment. This result significantly extends previous findings in both tumor growth modeling and the biofilm modeling field. Besides establishing local existence and uniqueness, we also prove the continuous dependence of the solution on initial and boundary data. Furthermore, global existence is deduced using a combination of invariance regions and energy estimates. The proof for local existence is obtained by utilizing fixed point arguments combined with semigroup theory.