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Travelling waves in a differential flow reactor with simple autocatalytic kinetics. (English) Zbl 0899.92038

Summary: A simple prototype model for a differential flow reactor in which the possible initiation and propagation of a reaction-diffusion-convection travelling-wave solution (TWS) in the simple isothermal autocatalytic system $A+mB\to \left(m+1\right)B$, rate $ka{b}^{m}\left(m\ge 1\right)$, is studied with special attention being paid to the most realistic cases $\left(m=1,2\right)$. The physical problem considered is such that the reactant $A$ (present initially at uniform concentration) is immobilised within the reactor. A reaction is then initiated by allowing the autocatalyst species to enter and to flow through the reaction region with a constant velocity.

The structure of the permanent-form travelling waves supported by the system is considered and a solution obtained valid when the flow rate (of the autocatalyst) is very large. General properties of the corresponding initial-value problem (IVP) are derived and it is shown that the TWS are the only long-time solutions supported by the system. Finally, these results are complemented with numerical solutions of the IVP which confirm the analytical results and allow the influence of the parameters of the problem not accessible to the theoretical analysis to be determined.

##### MSC:
 92E20 Classical flows, reactions, etc. 35K57 Reaction-diffusion equations 76V05 Interacting phases (fluid mechanics) 35K15 Second order parabolic equations, initial value problems 65N99 Numerical methods for BVP of PDE