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 |