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Shock solution to a class of quasilinear Robin boundary value problems. (Chinese. English summary) Zbl 1174.34345

Summary: A class of Robin boundary value problems is considered. Under suitable conditions, firstly, the formal outer solution of the original problem is constructed. Secondly, the shock layer corrective term is constructed via the transformation of stretched variable. Finally, the existence and uniform validity of the asymptotic expansion in the whole interval are proved by means of the theory of differential inequalities.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
34A40 Differential inequalities involving functions of a single real variable
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