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Hyperbolic Problems: Theory, Numerics, Applications pp 841–850Cite as

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Existence of travelling fronts for Nonlinear transport equations

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Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 141))

Abstract

We consider a nonlinear transport equation as a hyperbolic generalisation of the well-known reaction diffusion equation. We show the existence of strictly monotone travelling fronts for the three main types of the nonlinearity: the positive source term, the combustion law, and the bistable case. In the first case there is a whole interval of possible speeds containing its strictly positive minimum For subtangential nonlinearities we can express the minimal wave speed explicitly by a variational formula.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstraße 22-26, Leipzig, 04103, Germany

    Hartmut R. Schwetlick

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  1. Hartmut R. Schwetlick
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Editors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, Leipzig, 04103, Germany

    Heinrich Freistühler

  2. Institute of Analysis and Numerical Mathematics, Otto-von-Guericke-University, PSF 4120, Magdeburg, 39106, Germany

    Gerald Warnecke

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© 2001 Springer Basel AG

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Schwetlick, H.R. (2001). Existence of travelling fronts for Nonlinear transport equations. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_37

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  • DOI: https://doi.org/10.1007/978-3-0348-8372-6_37

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9538-5

  • Online ISBN: 978-3-0348-8372-6

  • eBook Packages: Springer Book Archive

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