A note on the small-time development of the solution to a coupled, nonlinear, singular reaction-diffusion system

Autores: J. A. Leach
Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 47, Nº 4, 2006, págs. 581-591
Idioma: inglés
DOI: 10.1017/s1446181100010154
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Resumen
- In this paper, we consider a coupled, nonlinear, singular (in the sense that the reaction terms in the equations are not Lipschitz continuous) reaction-diffusion system, which arises from a model of fractional order chemical autocatalysis and decay, with positive initial data. In particular, we consider the cases when the initial data for the the dimensionless concentration of the autocatalyst, , is of (a) or (b) at large (dimensionless distance), where and are constants. While initially the dimensionless concentration of the reactant, , is identically unity, we establish, by developing the small- (dimensionless time) asymptotic structure of the solution, that the support of becomes finite in infinitesimal time in both cases (a) and (b) above. The asymptotic form for the location of the edge of the support of as is given in both cases.