Stability, Relaxation, and Oscillation of Biodegradation Fronts

We study the stability and oscillation of traveling fronts in a three-component, advection-reaction biodegradation model. The three components are pollutant, nutrient, and bacteria concentrations. Under an explicit condition on the biomass growth and decay coefficients, we derive reduced, two-component, semilinear hyperbolic models through a relaxation procedure, during which biomass is slaved to pollutant and nutrient concentration variables. The reduced twocomponent models resemble the Broadwell model of the discrete velocity gas. The traveling fronts of the reduced system are explicit and are expressed in terms of hyperbolic tangent function in the nutrient-deficient regime. We perform energy estimates to prove the asymptotic stability of these fronts under explicit conditions on the coefficients in the system. In the small damping limit, we carry out Wentzel

• Type: Journal
• Year: 2000
• Where: SIAMAM
• Authors: Jack X. Xin, James M. Hyman
• Keywords: Advection-reaction Biodegradation Model, Explicit Conditions, Semilinear Hyperbolic Models, SIAMAM 2000