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Existence and uniqueness of discontinuous solutions for a hyperbolic system

  • Feimin Huang (a1)

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

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

6 F. 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.

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

10 D. 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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