Pan, Yafei; Ni, Mingkang; Davydova, M. A. 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. Reviewer: Dilmurat Tursunov (Osh) Cited in 11 Documents 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 Keywords:problem of reaction-diffusion-advection type; internal transition layer; asymptotic methods; problems with discontinuous nonlinearity PDFBibTeX XMLCite \textit{Y. Pan} et al., Math. Notes 104, No. 5, 735--744 (2018; Zbl 1432.34077); translation from Mat. Zametki 104, No. 5, 755--766 (2018) Full Text: DOI References: [1] N. N. Nefedov and M. K. Ni, “Internal layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term,” Zh. Vychisl.Mat. Mat. Fiz. 55 (12), 2042-2048 (2015) [Comput. Math. Math. Phys. 55 (12), 2001-2007 (2015)]. · Zbl 1367.34082 [2] N. T. Levashova, N. N. Nefedov, and A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term,” Zh. Vychisl. Mat. Mat. Fiz. 57 (5), 854-866 (2017) [Comput. Math. Math. Phys. 57 (5), 854-866 (2017)]. · Zbl 1372.35020 [3] Vasil’eva, A. B.; Butuzov, V. F.; Nefedov, N. N., Singularly perturbed problems with boundary and internal layers, 268-283 (2010), Moscow · Zbl 1207.35039 [4] N. N. Nefedov and M. A. Davydova, “Contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems,” Differ. Uravn. 48 (5), 738-748 (2012) [Differ. Equations 48 (5), 745-755 (2012)]. · Zbl 1257.35028 [5] N. N. Nefedov, L. Recke, and K. R. Schneider, “Existence and asymptotic stability of periodic solutions with an internal layer of reaction-advection-diffusion equations,” J. Math. Anal. Appl. 405 (1), 90-103 (2013). · Zbl 1325.35099 · doi:10.1016/j.jmaa.2013.03.051 [6] Davydova, M. A.; Nefedov, N. N., Existence and stability of contrast structures in multidimensional singularly perturbed reaction-diffusion-advection problems, 277-285 (2017), Cham · Zbl 1368.65219 [7] A. B. Vasil’eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations in Current Problems in Applied and Computational Mathematics (Vyssh. Shkola, Moscow, 1990) [in Russian]. · Zbl 0747.34033 [8] M. A. Davydova, “Existence and stability of solutions with boundary layers in multidimensional singularly perturbed reaction-diffusion-advection problems,” Mat. Zametki 98 (6), 853-864 (2015) [Math. Notes 98 (6), 909-919 (2015)]. · Zbl 1338.35144 · doi:10.4213/mzm10623 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.