A Quasi-linear, Singular Perturbation Problem of Hyperbolic Type

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Abstract
Using matched asymptotic expansions, a formal approximation can be constructed for an initial value problem of singularly perturbed, hyperbolic type in two independent variables. Under a time-like condition for the subcharacteristics of the unperturbed operator the correctness of the formal approximation is shown. Because of the nonlinearity of the perturbing hyperbolic operator, this work generalizes Geel [4]. The correctness proof is based on Schauder’s fixed point theorem; it uses existence, uniqueness and regularity theory for hyperbolic systems and a priori estimates for a solution analogous to Geel [4] as ingredients.

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