Well-posedness for a system of diffusion-reaction equations with noncoercive diffusion.

We prove that there is a unique solution for a system of diffusion-reaction equations, which occur when simulating microbiological growth at the pore scale with a high enough spatial resolution. Moreover, we show that the solution depends continuously on initial data. The diffusion for each component of the system is either coercive on Ω, only elliptic on a subset Ωi (and zero elsewhere), or zero everywhere. This yields a noncoercive diffusion operator for the system of partial differential equations. The reaction is assumed to be Lipschitz continuous. [ABSTRACT FROM AUTHOR]