Coexistence in the unstirred chemostat

摘要

We consider a rather general system of reaction diffusion equations containing multiple parameters and prove existence of positive solutions for some sets of parameters. The problem models long term coexistence of competing microorganisms in an unstirred chemostat with diffusion and flow. The proof, as in previous work, depends on a bifurcation argument using a Crandall-Rabinowitz theorem. Since stability of these steady states, as well as the more general question of persistence is unresolved, we include some numerical results which shed light on these questions.