Abstract
Reaction-diffusion equations are well-studied due to their common occurrence in many areas of chemistry, physics, biology and engineering (e.g. [1], [2]). Models for reaction-diffusion processes involving two chemical species have a long history and a large literature, and the interested reader is referred to the articles (and their reference lists) cited at the end. In this set of notes we consider the long-time dynamics of a one-dimensional reaction-diffusion front between two initially separated reactants (A,B), studied within the continuum, or mean-field, approximation for the case that reactant A is free to diffuse and reactant B is static (see figure 1). The reaction term studied is R(ρA,ρB) = kρM AρN B , where ρi denotes the concentration of species i, which allows for the possibility of higher-order kinetics.
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References
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© 2002 Springer Science+Business Media Dordrecht
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Bazant, M.Z., Stone, H.A. (2002). A Two-Species Reaction-Diffusion Problem with One Static Reactant: The Case of Higher Order Kinetics. In: Berestycki, H., Pomeau, Y. (eds) Nonlinear PDE’s in Condensed Matter and Reactive Flows. NATO Science Series, vol 569. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0307-0_1
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DOI: https://doi.org/10.1007/978-94-010-0307-0_1
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