A Geometric Construction of Traveling Waves in a Bioremediation Model |
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Authors: | M Beck A Doelman TJ Kaper |
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Institution: | (1) Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA;(2) Centrum voor Wiskunde en Informatica, 1090 BG, Amsterdam, The Netherlands |
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Abstract: | Bioremediation is a promising technique for cleaning contaminated soil. We study an idealized bioremediation model involving
a substrate (contaminant to be removed), electron acceptor (added nutrient), and microorganisms in a one-dimensional soil
column. Using geometric singular perturbation theory, we construct traveling waves (TW) corresponding to the motion of a biologically
active zone, in which the microorganisms consume both substrate and acceptor. For certain values of the parameters, the traveling
waves exist on a three-dimensional slow manifold within the five-dimensional phase space. We prove persistence of the slow
manifold under perturbation by controlling the nonlinearity via a change of coordinates, and we construct the wave in the
transverse intersection of appropriate stable and unstable manifolds in this slow manifold. We study how the TW depends on
the half-saturation constants and other parameters and investigate numerically a bifurcation in which the TW loses stability
to a periodic wave. |
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