Open AccessSINGULARLY PERTURBED REACTION‐DIFFUSION SYSTEMS IN CASES OF EXCHANGE OF STABILITIES
Author(s) -
BUTUZOV V.F.,
NEFEDOV N.N.,
SCHNEIDER K.R.
Publication year - 2000
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.2000.tb00035.x
Subject(s) - reaction–diffusion system , diffusion , method of matched asymptotic expansions , mathematics , singular perturbation , differential equation , reaction rate , thermodynamics , mathematical analysis , chemistry , physics , catalysis , biochemistry
. We study singularly perturbed elliptic and parabolic differential equations under the assumption that the associated equation has intersecting families of equilibria (exchange of stabilities). We prove by means of the method of asymptotic lower and upper solutions that the asymptotic behavior with respect to the small parameter changes near the curve of exchange of stabilities. The application of that result to systems modeling fast bimolecular reactions in a heterogeneous environment implies a transition layer (jumping behavior) of the reaction rate. This behavior has to be taken into account for identification problems in reaction systems.