Stability, relaxation, and oscillation of biodegradation fronts

Jack Xin James M Hyman

Analysis of PDEs mathscidoc:1912.43877

SIAM Journal on Applied Mathematics, 61, (2), 472-505, 2000
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 two-component 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--Kramers--Brillouin (WKB) analysis on front
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  title={Stability, relaxation, and oscillation of biodegradation fronts},
  author={Jack Xin, and James M Hyman},
  booktitle={SIAM Journal on Applied Mathematics},
Jack Xin, and James M Hyman. Stability, relaxation, and oscillation of biodegradation fronts. 2000. Vol. 61. In SIAM Journal on Applied Mathematics. pp.472-505.
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