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Loss of hyperbolicity changes the number of wave groups in Riemann problems

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Abstract

Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve foliation and a rarefaction curve foliation is necessary.

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Authors and Affiliations

  1. Centro de Matemática, Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    Vitor Matos

  2. Department of Computer Science, University of Calgary, ICT 602, 2500 University Dr NW Calgary, Alberta, T2N 1N4, Canada

    Julio D. Silva

  3. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Dan Marchesin

Authors
  1. Vitor Matos
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  2. Julio D. Silva
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  3. Dan Marchesin
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Corresponding author

Correspondence to Vitor Matos.

Additional information

Research supported by CNPq under grant PCI 170200/2014-0.

The author thanks the Foundation CMG Industrial Research Chair Program.

Research supported in part by CNPq under grants 402299/2012-4, 301564/2009-4 and 470635/ 2012-6, by FAPERJ under grants E-26/210.738/2014, E-26/201.210/2014, E-26/110.658/2012, E-26/111.369/2012,E-26/110.114/2013 andE-26/010.002762/2014,byANP under grantPRH32- 731948/2010, by Petrobras under grant PRH32-6000.0069459.11.4, as well as by CAPES under grant Nuffic-024/2011.

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Matos, V., Silva, J.D. & Marchesin, D. Loss of hyperbolicity changes the number of wave groups in Riemann problems. Bull Braz Math Soc, New Series 47, 545–559 (2016). https://doi.org/10.1007/s00574-016-0168-4

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  • DOI: https://doi.org/10.1007/s00574-016-0168-4

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