Abstract
We study reaction-diffusion equations with a spatially inhomogeneous reaction term. If the coefficient of these reaction term is much larger than the diffusion coefficient, a sharp interface appears between two different phases. We show that the equation of motion of such an interface involves a drift term despite the absence of drift in the original diffusion equations. In particular, we show that the same rich spatial patterns observed for a chemotaxis-growth model can be realized by a system without a drift term.
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Nakamura, KI., Matano, H., Hilhorst, D. et al. Singular Limit of a Reaction-Diffusion Equation with a Spatially Inhomogeneous Reaction Term. Journal of Statistical Physics 95, 1165–1185 (1999). https://doi.org/10.1023/A:1004518904533
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DOI: https://doi.org/10.1023/A:1004518904533