Global existence for reaction-diffusion systems modelling ignition



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Herrero, Miguel A. and Lacey, Andrew A. and Velázquez, J.J. L. (1998) Global existence for reaction-diffusion systems modelling ignition. Archive for Rational Mechanics and Analysis, 142 (3). pp. 219-251. ISSN 0003-9527

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The pair of parabolic equations u(t) = a Δ u + f(u,v), (1) v(t) = b Δ b - f(u, v), (2) with a > 0 and b > 0 models the temperature and concentration for an exothermic chemical reaction for which just one species controls the reaction rate f. Of particular interest is the case where f(u, v)= ve(u), (3) which appears in the Frank-Kamenetskii approximation to Arrhenius-type reactions, We show here that for a large choice of the nonlinearity f(u,v) in (1), (2) (including the model case (3)), the corresponding initial-value problem for(1), (2) in the whole space with bounded initial data has a solution which exists for all times. Finite-time blow-up might occur, though, for other choices of function f(ld, v), and we discuss here a linear example which strongly hints at such behaviour.

Item Type:Article
Uncontrolled Keywords:Semilinear heat-equation; blow-up; boundedness
Subjects:Sciences > Mathematics > Differential equations
ID Code:16949
Deposited On:31 Oct 2012 09:09
Last Modified:12 Dec 2018 15:07

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