EVENT DETAILS AND ABSTRACT

Title: Dynamics of patterns in activator-inhibitor systems
Speaker: Prof. Tasso Kaper
Speaker Info: Boston University
Brief Description:
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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 analytical and geometric singular perturbation theory, we study traveling waves (TW) corresponding to motion of a biologically active zone, in which the microorganisms consume both substrate and acceptor. We construct them using both matched asymptotic expansions and invariant manifold theory, showing that they lie in the transverse intersection of appropriate stable and unstable manifolds. We also study how the TWs depend on the physical parameters, including the half saturation constants in the reaction kinetics, and we investigate a bifurcation in which these TWs lose stability to time-periodic TWs.