Herrero, Miguel A.Lacey, Andrew A.Velázquez, J.J. L.2023-06-202023-06-201998-070003-952710.1007/s002050050091https://hdl.handle.net/20.500.14352/57666The 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.engjournal articlehttp://www.springerlink.com/content/mq3y2ugwfqk5qc3l/fulltext.pdfhttp://www.springerlink.comrestricted access536.2517.956.4Semilinear heat-equationblow-upboundednessEcuaciones diferenciales1202.07 Ecuaciones en Diferencias