Singular Perturbations of Limit Points with Application to Tubular Chemical Reactors

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.