Mathematical analysis of a model describing the invasion of bacteria in burn wounds

We investigate a reaction-diffusion system comprising a parabolic equation coupled with an ordinary differential equation on an unbounded space domain. This system arises as a model for host tissue degradation by bacteria and involves a parameter describing the degradation rate that is typically very large. We prove the existence and uniqueness of solutions to this system and the convergence to a Stefan-like free boundary problem as the degradation rate tends to infinity.