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Singular Perturbations of Limit Points with Application to Tubular Chemical Reactors
Author(s) -
Lange Charles G.,
Weinitschke Hubertus J.
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19918417
Subject(s) - singular perturbation , limit (mathematics) , perturbation (astronomy) , mathematical analysis , mathematics , rotational symmetry , nonlinear system , limit point , singular solution , boundary value problem , singular point of a curve , perturbation theory (quantum mechanics) , asymptotic expansion , asymptotic analysis , physics , geometry , quantum mechanics
Singular perturbation techniques are used to study solutions of certain nonlinear boundary‐value problems defined on domains with a circular hole of radius ε, in the limit ε → 0. Asymptotic expansions are constructed to describe the behavior of solutions at and near simple and double limit points (cusps). In particular, the behavior of axisymmetric solutions in an annular domain at limit points is investigated. The results are applied to two model problems arising in chemical‐reactor theory. The asymptotic analysis predicts a surprisingly large sensitivity of limit points to the ε‐domain perturbation considered here.