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The Structure of Shock Waves in Dissipative Hyperbolic Models

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From Particle Systems to Partial Differential Equations II

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 129))

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Abstract

The study is devoted to the shock structure problem in hyperbolic systems of balance laws, where the dissipation is taken into account through relaxation. These models typically arise by extending the set of state variables, as well as governing equations. The existence of physically admissible solution is related to stability properties of equilibrium states and their transcritical bifurcation. The main examples will be the hyperbolic model of isothermal viscoelasticity, 13 moments equations for monatomic gases and the binary mixture of non-reacting ideal gases. The problems which arise in models with mixed type of dissipation, i.e. both relaxation and diffusion, are tackled as well.

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Acknowledgments

This work was supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, through the project “Mechanics of nonlinear and dissipative systems—contemporary models, analysis and applications”, Project No. ON174016.

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Authors and Affiliations

  1. Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000, Novi Sad, Serbia

    Srboljub Simić

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  1. Srboljub Simić
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Correspondence to Srboljub Simić .

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Editors and Affiliations

  1. Centre of Mathematics, University of Minho, Braga, Portugal

    Patrícia Gonçalves

  2. Centre of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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Simić, S. (2015). The Structure of Shock Waves in Dissipative Hyperbolic Models. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations II. Springer Proceedings in Mathematics & Statistics, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-319-16637-7_13

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