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Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions
Author(s) -
Guo Lihui,
Zhang Ying,
Yin Gan
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3209
Subject(s) - classification of discontinuities , chaplygin gas , riemann hypothesis , shock wave , delta , piecewise , mathematics , dirac delta function , mathematical analysis , euler equations , shock (circulatory) , euler's formula , mathematical physics , riemann problem , physics , classical mechanics , mechanics , quantum mechanics , medicine , cosmology , astronomy , dark energy
In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.