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 , only elliptic on a subset (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.