RT Journal Article
T1 Global existence for reaction-diffusion systems modelling ignition
A1 Herrero, Miguel A.
A1 Lacey, Andrew A.
A1 Velázquez, J.J. L.
AB 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.
PB Springer
SN 0003-9527
YR 1998
FD 1998-07
LK https://hdl.handle.net/20.500.14352/57666
UL https://hdl.handle.net/20.500.14352/57666
LA eng
DS Docta Complutense
RD 6 abr 2025