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

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.