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In this work, we study the mathematical analysis of a coupled system of tworeaction-diffusion-advection equations and Danckwerts boundary conditions,which models the interaction between a microbial population (e.g., bacterias)and a diluted substrate (e.g., nitrate) in a continuous flow bioreactor. Thistype of bioreactor can be used, for instance, for water treatment. First, weprove the existence and uniqueness of solution, under the hypothesis of linearreaction by using classical results for linear parabolic boundary valueproblems. Next, we prove the existence and uniqueness of solution for somenonlinear reactions by applying \textit{Schauder Fixed Point Theorem} and thetheorem obtained for the linear case. Results about the nonnegativeness andboundedness of the solution are also proved here.

Existence and Uniqueness of Solution of a Continuous Flow Bioreactor Model with Two Species