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Asymptotic-Numerical Method for Moving Fronts in Two-Dimensional R-D-A Problems

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Finite Difference Methods,Theory and Applications (FDM 2014)

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Abstract

A singularly perturbed initial-boundary value problem for a parabolic equation known in applications as the reaction-diffusion equation is considered. An asymptotic expansion of the solution with moving front is constructed. Using the asymptotic method of differential inequalities we prove the existence and estimate the asymptotic expansion for such solutions. The method is based on well-known comparison theorems and formal asymptotics for the construction of upper and lower solutions in singularly perturbed problems with internal and boundary layers.

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References

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Acknowledgements

This work is supported by RFBR, pr. N 13-01-00200.

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Authors and Affiliations

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

    Vladimir Volkov, Nikolay Nefedov & Eugene Antipov

Authors
  1. Vladimir Volkov
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  2. Nikolay Nefedov
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  3. Eugene Antipov
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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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Volkov, V., Nefedov, N., Antipov, E. (2015). Asymptotic-Numerical Method for Moving Fronts in Two-Dimensional R-D-A Problems. 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_46

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  • DOI: https://doi.org/10.1007/978-3-319-20239-6_46

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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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