On a singular initial-boundary-value problem for a reaction-diffusion equation arising from a simple model of isothermal chemical autocatalysis
1992 ◽
Vol 437
(1901)
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pp. 657-671
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Keyword(s):
In this paper we examine the evolution that occurs when a localized input of an autocatalyst B is introduced into an expanse of a reactant A. The reaction is autocatalytic of order p,so A -> B at rate k [A] [B] p with rate constant k . We examine the case when 0 < p < 1, with p>/ 1 having been examined by Needham & Merkin (Phil. Trans. R. Soc. Lond. A 337, 261—274 (1991)). In particular, we show that the fully reacted state is not achieved (as t-> oo) via the propagation of a travelling wavefront (as for p>/ 1) but is approached uniformly in space as t-00.
2012 ◽
Vol 52
(6)
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pp. 926-931
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2009 ◽
Vol 9
(1)
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pp. 100-110
1994 ◽
Vol 15
(3)
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pp. 267-273
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
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1995 ◽
Vol 350
(1694)
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pp. 335-360
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Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences
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1994 ◽
Vol 348
(1687)
◽
pp. 229-260
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2013 ◽
Vol 25
(1)
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pp. 9-26
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2002 ◽
Vol 55
(4)
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pp. 511-560
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1993 ◽
Vol 03
(01)
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pp. 79-95
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