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On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers

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Finite Difference Methods,Theory and Applications (FDM 2014)

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Abstract

In this paper we present a further development of our asymptotic comparison principle, applying it for some new important classes of initial boundary value problem for the nonlinear singularly perturbed time periodic parabolic equations, which are called in applications as reaction-diffusion-advection equations. We illustrate our approach for the new problem with balanced nonlinearity. The theorems, which states the existence of the periodic solution with internal layer, gives it’s asymptotic approximation and state their Lyapunov stability are proved.

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Acknowledgements

This work is supported by RFBR, pr. N 13-01-91333.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Nikolay Nefedov & Aleksei Yagremtsev

Authors
  1. Nikolay Nefedov
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  2. Aleksei Yagremtsev
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Corresponding author

Correspondence to Nikolay Nefedov .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Sofia, Bulgaria

    Ivan Dimov

  2. Institue of Mathematics and MTA-ELTE Numerical Analysis and Large Networks Research Group, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Nefedov, N., Yagremtsev, A. (2015). On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods,Theory and Applications. FDM 2014. Lecture Notes in Computer Science(), vol 9045. Springer, Cham. https://doi.org/10.1007/978-3-319-20239-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20238-9

  • Online ISBN: 978-3-319-20239-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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