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    Li, Xiumei and Shen, Chun 2013. Viscous Regularization of Delta Shock Wave Solution for a Simplified Chromatography System. Abstract and Applied Analysis, Vol. 2013, p. 1.

    Kalisch, Henrik and Mitrović, Darko 2012. Singular solutions of a fully nonlinear 2 × 2 system of conservation laws. Proceedings of the Edinburgh Mathematical Society, Vol. 55, Issue. 03, p. 711.

    Mitrovic, D. Bojkovic, V. and Danilov, V. G. 2009. Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process. Mathematical Methods in the Applied Sciences, p. n/a.

    Danilov, V.G. and Mitrovic, D. 2008. Delta shock wave formation in the case of triangular hyperbolic system of conservation laws. Journal of Differential Equations, Vol. 245, Issue. 12, p. 3704.

    Feimin, Huang 1998. On the two-dimensional cauchy problem of a hyperbolic system. Acta Mathematica Sinica, Vol. 14, Issue. 3, p. 399.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 127, Issue 6
  • January 1997, pp. 1193-1205

Existence and uniqueness of discontinuous solutions for a hyperbolic system

  • Feimin Huang (a1)
  • DOI:
  • Published online: 14 November 2011

In this paper, we prove the global existence and uniqueness of solutions to the Cauchy problem of a hyperbolic system, which probably contains so-called δ-waves.

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3A. Forestier and P. LeFloch . Multivalued solutions to some non-linear and non-strictly hyperbolic systems. Japan. J. Indust. Appl. Math. 9 (1992), 123.

4E. Hopf . The partial differential equation ut, + uux = μuxx. Comm. Pure Appl. Math. 3 (1950), 201–30.

6F. Huang , C. Li and Z. Wang . Solutions containing delta-waves of Cauchy problems for a nonstrictly hyperbolic system. Acta Mathematicae Applicatae Sinica 11 (1995), 429–46.

7P. Lax . Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math. 10 (1957), 537–66.

10D. Tan , T. Zheng and Y. Zhang . Delta-shock wave as limits of vanishing viscosity for hyperbolic systems of conservation laws. J. Differential Equations 112 (1994), 132.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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