Existence of traveling waves in a biodegradation model for organic contaminants

Regan Murray Jack Xin

Analysis of PDEs mathscidoc:1912.43884

SIAM journal on mathematical analysis, 30, (1), 72-94, 1998
We study a biodegradation model for the time evolution of concentrations of contaminant, nutrient, and bacteria. The bacteria has a natural concentration which will increase when the nutrient reaches the substrate (contaminant). The growth utilizes nutrients and degrades the substrate. Eventually, such a process removes all the substrate and can be described by traveling wave solutions. The model consists of advection-reaction-diffusion equations for the substrate and nutrient concentrations and a rate equation (ODE) for the bacteria concentration. We first show the existence of approximate traveling wave solutions to an elliptically regularized system posed on a finite domain using degree theory and the elliptic maximum principle. To prove that the approximate solutions do not converge to trivial solutions, we construct comparison functions for each component and employ integral identities of the governing
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@inproceedings{regan1998existence,
  title={Existence of traveling waves in a biodegradation model for organic contaminants},
  author={Regan Murray, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210432015560448},
  booktitle={SIAM journal on mathematical analysis},
  volume={30},
  number={1},
  pages={72-94},
  year={1998},
}
Regan Murray, and Jack Xin. Existence of traveling waves in a biodegradation model for organic contaminants. 1998. Vol. 30. In SIAM journal on mathematical analysis. pp.72-94. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210432015560448.
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