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

  • Dmitry Lukyanenko
  • Nikolay NefedovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

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.

Keywords

Blow-up phenomena Burgers equation Singularly perturbed Interior layer Richardson extrapolation 

Notes

Acknowledgements

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

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of PhysicsLomonosov Moscow State UniversityMoscowRussia

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