Travelling fronts for multidimensional nonlinear transport equations

Hartmut R. Schwetlick

doi:10.1016/S0294-1449(00)00127-X

Travelling fronts for multidimensional nonlinear transport equations

Hartmut R. Schwetlick

Research output: Contribution to journal › Article › peer-review

25 Citations (SciVal)

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 give an explicit expression for the minimal wave speed.

Original language	English
Pages (from-to)	523-550
Number of pages	28
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	17
Issue number	4
DOIs	https://doi.org/10.1016/S0294-1449(00)00127-X
Publication status	Published - 1 Jul 2000

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/S0294-1449(00)00127-XLicence: CC BY

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AB - 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 give an explicit expression for the minimal wave speed.

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ER -

Travelling fronts for multidimensional nonlinear transport equations

Abstract

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