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Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification: Asymptotics and Numerical Diagnostics

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Finite Difference Methods. Theory and Applications (FDM 2018)

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

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Abstract

This work develops a theory of asymptotic-numerical investigations of moving fronts in reaction-diffusion-advection models. We present the result of consideration of singularly perturbed parabolic Burgers-type equations with nonlinear forcing. Conditions of solution blow-up are formulated. Numerical algorithm which allows to recognise and describe the solutions blow-up is presented. In particular, in order to demonstrate the proposed method, we apply our approach to the problem with cubic forcing.

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Acknowledgements

The work was supported by the Russian Science Foundation [grant number 18-11-00042].

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Authors and Affiliations

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

    Dmitry Lukyanenko & Nikolay Nefedov

Authors
  1. Dmitry Lukyanenko
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  2. Nikolay Nefedov
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Corresponding author

Correspondence to Nikolay Nefedov .

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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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Lukyanenko, D., Nefedov, N. (2019). Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification: Asymptotics and Numerical Diagnostics. 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_7

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

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