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Titolo:
GLOBAL EXISTENCE FOR REACTION-DIFFUSION SYSTEMS MODELING IGNITION
Autore:
HERRERO MA; LACEY AA; VELAZQUEZ JJL;
Indirizzi:
UNIV COMPLUTENSE MADRID,FAC MATH,DEPT MATEMAT APLICADA E-28040 MADRIDSPAIN HERIOT WATT UNIV,DEPT MATH EDINBURGH EH14 4AS MIDLOTHIAN SCOTLAND
Titolo Testata:
Archive for Rational Mechanics and Analysis
fascicolo: 3, volume: 142, anno: 1998,
pagine: 219 - 251
SICI:
0003-9527(1998)142:3<219:GEFRSM>2.0.ZU;2-N
Fonte:
ISI
Lingua:
ENG
Soggetto:
SEMILINEAR HEAT-EQUATION; BLOW-UP; BOUNDEDNESS;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Science Citation Index Expanded
Citazioni:
25
Recensione:
Indirizzi per estratti:
Citazione:
M.A. Herrero et al., "GLOBAL EXISTENCE FOR REACTION-DIFFUSION SYSTEMS MODELING IGNITION", Archive for Rational Mechanics and Analysis, 142(3), 1998, pp. 219-251

Abstract

The pair of parabolic equations u(t) = a Delta u + f(u,v), (1) v(t) =b Delta 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 thecase where f(u, v)= ve(u), (3) which appears in the Frank-Kamenetskiiapproximation to Arrhenius-type reactions, We show here that for a large choice of the nonlinearity f(u,v) in (1), (2) (including the modelcase (3)), the corresponding initial-value problem for(1), (2) in thewhole space with bounded initial data has a solution which exists forall times. Finite-time blow-up might occur, though, for other choicesof function f(ld, v), and we discuss here a linear example which strongly hints at such behaviour.

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Documento generato il 20/09/20 alle ore 03:54:20