EXISTENCE OF TRAVELING WAVES IN A BIODEGRADATION MODEL FOR ORGANIC CONTAMINANTS

We study a biodegradation model for the time evolution of concentratio ns of contaminant, nutrient, and bacteria. The bacteria has a natural concentration which will increase when the nutrient reaches the substr ate (contaminant). The growth utilizes nutrients and degrades the subs trate. Eventually, such a process removes all the substrate and can be described by traveling wave solutions. The model consists of advectio n-reaction-diffusion equations for the substrate and nutrient concentr ations and a rate equation (ODE) for the bacteria concentration. We fi rst show the existence of approximate traveling wave solutions to an e lliptically regularized system posed on a finite domain using degree t heory and the elliptic maximum principle. To prove that the approximat e solutions do not converge to trivial solutions, we construct compari son functions for each component and employ integral identities of the governing equations. This way, we derive a priori estimates of soluti ons independent of the length of the finite domain and the regularizat ion parameter. The integral identities take advantage of the forms of coupling in the system and help us obtain optimal bounds on the travel ing wave speed. We then extend the domain to the infinite line limit, remove the regularization, and construct a traveling wave solution for the original set of equations satisfying the prescribed boundary cond itions at spatial infinities. The contaminant and nutrient profiles of the traveling waves are strictly monotone functions, while the biomas s profile has a pulse shape.