INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS | Zendy

Yanyan Zhang | Zendy; Yu Zhang | Zendy

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INTERACTIONS OF DELTA SHOCK WAVES FOR A CLASS OF NONSTRICTLY HYPERBOLIC SYSTEM OF CONSERVATION LAWS

Author(s) -

Yanyan Zhang,

Yu Zhang

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20190228

Subject(s) - conservation law , dirac delta function , riemann hypothesis , riemann problem , shock wave , delta , rarefaction (ecology) , discontinuity (linguistics) , mathematical analysis , physics , mathematics , function (biology) , mathematical physics , classical mechanics , mechanics , geology , paleontology , astronomy , evolutionary biology , biology , species richness

In this paper, we study the perturbed Riemann problem for a class of nonstrictly hyperbolic system of conservation laws, and focuse on the interactions of delta shock waves with the shock waves and the rarefaction waves. The global solutions are constructed completely with the method of splitting delta function. In solutions, we find a new kind of nonclassical wave, which is called delta contact discontinuity with Dirac delta function in both components. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. Moreover, by letting perturbed parameter ε tend to zero, we analyze the stability of Riemann solutions.

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