Introduction to Singular Perturbation Problems

Abstract

Mathematical models used in physics often lead to problems which do not have explicit solutions. Their numerical solutions become more difficult when small parameters are present or when the calculation domains are very large. In such cases, simpler models can be developed either by setting a parameter to zero or by restricting the study to a smaller domain. When a small parameter, denoted by ɛ, is set to zero, it is possible that the solution of the initial problem does not tend uniformly to the solution of the reduced problem as ɛ → 0. A singular perturbation problem arises for which difficult mathematical questions need to be addressed.