Computational and Applied Mathematics

, Volume 37, Issue 2, pp 1721–1736 | Cite as

Riemann solutions for counterflow combustion in light porous foam

  • Grigori ChapiroEmail author
  • Laura Senos


The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented.


Traveling wave Riemann problem Counterflow combustion Porous medium 

Mathematics Subject Classification

80A25 35C07 35K57 34C37 



The authors would like to thank Prof. S. Schecter and Prof. D. Marchesin for the preliminary work. We also would like to thank Prof. D. Tadeu, I. Ledoino and D. L. de Albuquerque for developing and improving the numerical code RCD used in this work. We thank anonymous referee for help in improving this text.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Juiz de ForaJuiz de ForaBrazil

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