Abstract:
The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.
Citation:
M. A. Davydova, S. A. Zakharova, N. T. Levashova, “On one model problem for the reaction-diffusion-advection equation”, Zh. Vychisl. Mat. Mat. Fiz., 57:9 (2017), 1548–1559; Comput. Math. Math. Phys., 57:9 (2017), 1528–1539
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\paper On one model problem for the reaction-diffusion-advection equation
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\yr 2017
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\issue 9
\pages 1548--1559
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\jour Comput. Math. Math. Phys.
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\vol 57
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\pages 1528--1539
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Linking options:
https://www.mathnet.ru/eng/zvmmf10617
https://www.mathnet.ru/eng/zvmmf/v57/i9/p1548
This publication is cited in the following 9 articles:
A. A. Bykov, “Evolution of a Two-Dimensional Moving Contrast Structure in an Inhomogeneous Medium with Advection”, Moscow Univ. Phys., 79:2 (2024), 140
K. A. Kotsubinsky, N. T. Levashova, A. A. Melnikova, “Stabilization of a traveling front solution in a reaction-diffusion equation”, Mosc. Univ. Phys. Bull., 76:6 (2021), 413–423
N. T. Levashova, B. V. Tischenko, “Existence and stability of the solution to a system of two nonlinear diffusion equations in a medium with discontinuous characteristics”, Comput. Math. Math. Phys., 61:11 (2021), 1811–1833
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Diffusion chaos and its invariant numerical characteristics”, Theoret. and Math. Phys., 203:1 (2020), 443–456
M. A. Davydova, N. N. Nefedov, S. A. Zakharova, Lecture Notes in Computer Science, 11386, Finite Difference Methods. Theory and Applications, 2019, 216
A. O. Orlov, N. T. Levashova, N. N. Nefedov, “Solution of contrast structure type for a parabolic reaction-diffusion problem in a medium with discontinuous characteristics”, Differ. Equ., 54:5 (2018), 669–686
N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem
in the case of balanced advection”, Izv. Math., 82:5 (2018), 984–1005
S. V. Bytsyura, N. T. Levashova, “Verkhnee i nizhnee resheniya dlya sistemy uravnenii tipa FitsKhyu–Nagumo”, Model. i analiz inform. sistem, 25:1 (2018), 33–53
Levashova N.T., Nefedov N.N., Nikolaeva O.A., Orlov A.O., Panin A.A., “The Solution With Internal Transition Layer of the Reaction-Diffusion Equation in Case of Discontinuous Reactive and Diffusive Terms”, Math. Meth. Appl. Sci., 41:18, SI (2018), 9203–9217
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