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The singular solutions to a nonsymmetric system of Keyfitz‐Kranzer type with initial data of Riemann type
Author(s) -
Sun Meina
Publication year - 2019
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.5939
Subject(s) - riemann problem , riemann hypothesis , mathematics , shock wave , mathematical analysis , discontinuity (linguistics) , riemann's differential equation , hodograph , rarefaction (ecology) , plane wave , type (biology) , riemann xi function , physics , mechanics , quantum mechanics , geology , paleontology , species richness
The solutions to the Riemann problem for a nonsymmetric system of Keyfitz‐Kranzer type are constructed explicitly when the initial data are located in the quarter phase plane. In particular, some singular hyperbolic waves are discovered when one of the Riemann initial data is located on the boundary of the quarter phase plane, such as the delta shock wave and some composite waves in which the contact discontinuity coincides with the shock wave or the wave back of rarefaction wave. The double Riemann problem for this system with three piecewise constant states is also considered when the delta shock wave is involved. Furthermore, the global solutions to the double Riemann problem are constructed through studying the interaction between the delta shock wave and the other elementary waves by using the method of characteristics. Some interesting nonlinear phenomena are discovered during the process of constructing solutions; for example, a delta shock wave is decomposed into a delta contact discontinuity and a shock wave.