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A class of shock solutions for the semilinear singularly perturbed boundary value problem. (English) Zbl 1085.65066

Summary: The shock solution for the semilinear singularly perturbed two-point boundary value problem is studied. Under suitable conditions and using the theory of differential inequalities, the existence and asymptotic behavior of the solution for the original boundary value problems are discussed. An uniformly effective asymptotic expansion and an estimation of solution \(u(x,\varepsilon)\) are obtained.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations