Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process | Zendy

Mitrovic D. | Zendy; Bojkovic V. | Zendy; Danilov V. G. | Zendy

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Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process

Author(s) -

Mitrovic D.,

Bojkovic V.,

Danilov V. G.

Publication year - 2009

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.1226

Subject(s) - conservation law , mathematics , riemann hypothesis , riemann problem , linearization , shock wave , diagonal , linear system , law , mathematical analysis , nonlinear system , geometry , physics , mechanics , quantum mechanics , political science

Using the weak asymptotic method, we approximate a triangular system of conservation laws arising from the so‐called generalized pressureless gas dynamics by a diagonal linear system. Then, we apply the usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how the delta shock wave naturally arises along the characteristics. Also, we propose a procedure that could be applied to more general systems of conservation laws. Copyright © 2009 John Wiley & Sons, Ltd.

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