Acta Mathematicae Applicatae Sinica

, Volume 11, Issue 4, pp 429–446 | Cite as

Solutions containing delta-waves of Cauchy problems for a nonstrictly hyperbolic system

  • Huang Feimin 
  • Li Caizhong 
  • Wang Zhen 


In this paper, we prove the global existence and uniqueness of generalized solution defined by Lebesgue-Stieltjes integral containing the so calledδ-wave for Cauchy problems of a nonstrictly hyperbolic system, and obtain some interesting properties of theδ-wave.

Key words

Hyperbolic system generalized solution δ-wave Lebesgue-Stieltjes integral 


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  1. [1]
    Xiaxi Ding. On a Non-strictly Hyperbolic System. Preprint, Dept. of Math. University of Jyvaskyla, No. 167, 1993.Google Scholar
  2. [2]
    Xiaxi Ding and Zheng Wang. Existence and Uniqueness of Discontinuous Solutions Defined by Lebesgue-Stieltjes Integral. Preprint.Google Scholar
  3. [3]
    E. Hopf. The Partial Differential Equationu t+uu x=μu xx.Comm. Pure Appl. Math., 1950, 3: 201–230.Google Scholar
  4. [4]
    Caizhong Li and Xiaozhou Yang. Riemann Problems of a Class of Non-strictly Hyperbolic Equations. Preprint.Google Scholar
  5. [5]
    D. Tan, T. Zhang and Y. Zheng. Delta-shock Wave as Limits of Vanishing Viscosity for Hyperbolic Systems of Consavation Laws.Journal of Diff. Eqs., 1994, 112(1), 1–32.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1995

Authors and Affiliations

  • Huang Feimin 
    • 1
    • 2
  • Li Caizhong 
    • 3
    • 4
  • Wang Zhen 
    • 5
    • 6
  1. 1.Institute of MathematicsShantou UniversityShantouChina
  2. 2.Institute of Applied Mathematicsthe Chinese Academy of ScienceBeijingChina
  3. 3.Institute of MathematicsShantou UniversityShantouChina
  4. 4.Department of Applied MathematicsSichuan United UniversityChengduChina
  5. 5.Institute of MathematicsShantou UniversityShantouChina
  6. 6.Wuhan Institute of Mathematical Physicsthe Chinese Academy of ScienceWuhanChina

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