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Accelerating fronts in autocatalysis
Optimization| Speaker: | Marcel Oliver, Tubingen |
| Location: | 202 Wellman |
| Start time: | Fri, Oct 13 2000, 4:10PM |
Description
We consider a reaction-diffusion system modelling propagating fronts
of an autocatalytic reaction of order $m$ in a one-dimensional,
infinitely extended medium. The Lewis number, i.e. the ratio of the
molecular diffusivity of the autocatalyst to that of the reactant, is
arbitrary. We prove that if the initial profile of the front decays
exponentially or algebraically with exponent $mu>1/(m-1)$, the speed
of the front is bounded for all times. Our method relies on weighted
Lebesgue and Sobolev-space estimates, from which we can reconstruct
pointwise results for the decay of the front via interpolation. The
result gives a functional analytic foundation and an extension to
arbitrary Lewis numbers to the numerical studies of Sherratt &
Marchant (IMA J. Appl. Math. extbf{56}, 1996, pp. 289--302) and
the asymptotic analysis of Needham & Barnes (Nonlinearity
extbf{12}, 1999, pp. 41--58).