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Contrast structures in problems for a stationary equation of reaction-diffusion-advection type with discontinuous nonlinearity. (English. Russian original) Zbl 1432.34077

Math. Notes 104, No. 5, 735-744 (2018); translation from Mat. Zametki 104, No. 5, 755-766 (2018).
In this article, a singularly perturbed boundary-value problem for a nonlinear stationary equation of reaction-diffusion-advection type is studied. A new class of problems with discontinuous advective and reactive terms is considered. The existence of contrast structures in problems of this type is proved, and an asymptotic approximation of the solution with an internal transition layer of arbitrary order of accuracy is obtained. New original scientific results have been obtained that can be applied in other fields of science and technology.

MSC:

34E15 Singular perturbations for ordinary differential equations
34A36 Discontinuous ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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References:

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