This article is cited in 7 scientific papers (total in 7 papers)
Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term
N. N. Nefedova, Minkang Nib
a Faculty of Physics, Moscow State University, Moscow, 119991, Russia
b East China Normal University, Shanghai, 200241, People's Republic of China
A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction–diffusion equation is studied. A new class of problems is considered, namely, problems with nonlinearity having discontinuities localized in some domains, which leads to the formation of sharp transition layers in these domains. The existence of solutions with an internal transition layer is proved, and their asymptotic expansion is constructed.
singular perturbations, one-dimensional reaction–diffusion equation, internal layers, asymptotic methods.
PDF file (99 kB)
Computational Mathematics and Mathematical Physics, 2015, 55:12, 2001–2007
N. N. Nefedov, Minkang Ni, “Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term”, Zh. Vychisl. Mat. Mat. Fiz., 55:12 (2015), 2042–2048; Comput. Math. Math. Phys., 55:12 (2015), 2001–2007
Citation in format AMSBIB
\by N.~N.~Nefedov, Minkang~Ni
\paper Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
N. T. Levashova, O. A. Nikolaeva, “Asimptoticheskoe issledovanie resheniya uravneniya teploprovodnosti vblizi granitsy razdela dvukh sred”, Model. i analiz inform. sistem, 24:3 (2017), 339–352
N. T. Levashova, N. N. Nefedov, A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term”, Comput. Math. Math. Phys., 57:5 (2017), 854–866
M. Ni, Ya. Pang, N. T. Levashova, O. A. Nikolaeva, “Internal layers for a singularly perturbed second-order quasilinear differential equation with discontinuous right-hand side”, Differ. Equ., 53:12 (2017), 1567–1577
Yafei Pan, Min Kan Ni, M. A. Davydova, “Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity”, Math. Notes, 104:5 (2018), 735–744
Pang Yafei, Ni Mingkang, N. T. Levashova, “Internal layer for a system of singularly perturbed equations with discontinuous right-hand side”, Differ. Equ., 54:12 (2018), 1583–1594
N. N. Nefedov, N. T. Levashova, A. O. Orlov, “The asymptotic stability of a stationary solution with an internal transition layer to a reaction-diffusion problem with a discontinuous reactive term”, Mosc. Univ. Phys. Bull., 73:6 (2018), 565–572
Qi X. Ni M., “On the Asymptotic Solution to a Type of Piecewise-Continuous Second-Order Dirichlet Problems of Tikhonov System”, J. Appl. Anal. Comput., 9:1 (2019), 105–117
|Number of views:|