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International Conference on Finite Difference Methods

FDM 2018: Finite Difference Methods. Theory and Applications pp 216–224Cite as

Asymptotically Lyapunov-Stable Solutions with Boundary and Internal Layers in the Stationary Reaction-Diffusion-Advection Problems with a Small Transfer

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

Abstract

The stationary reaction-diffusion-advection problems, modeling the processes of the transport and chemical transformation of active and passive impurities in the surface layer of the atmosphere, to which the asymptotic methods are applicable (to the problems), are considered. We study the multidimensional asymptotically Lyapunov-stable solutions of the boundary layer type and the contrast structures by constructing the formal asymptotic approximations of an arbitrary-order accuracy based on the boundary-function method. To justify the constructed asymptotics, we use an asymptotic method of differential inequalities. The results of the study are illustrated by the example of the two-dimensional boundary value problem with a cubic nonlinearity. They can be used to create a numerical algorithm that uses asymptotic analysis to construct spatially inhomogeneous mashes when describing the internal layer of contrast structure, and also for the purposes of constructing the test examples.

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Acknowledgements

This work was supported by the Russian Science Foundation (project no. 18-11-00042).

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    M. A. Davydova, N. N. Nefedov & S. A. Zakharova

Authors
  1. M. A. Davydova
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  2. N. N. Nefedov
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  3. S. A. Zakharova
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Corresponding author

Correspondence to M. A. Davydova .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Davydova, M.A., Nefedov, N.N., Zakharova, S.A. (2019). Asymptotically Lyapunov-Stable Solutions with Boundary and Internal Layers in the Stationary Reaction-Diffusion-Advection Problems with a Small Transfer. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_23

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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