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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 - 2010
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.