Analysis of singularities and development of shocks for a class of multidimensional hyperbolic systems of conservation laws

作者：Dai, WR; Kong, DX^*

来源：Mathematical Methods in the Applied Sciences, 2005, 28(13): 1585-1611.

DOI：10.1002/mma.628

• multidimensional Keyfitz-Kranzer system
• simple system
• blow-up
• blow-up rate
• shock wave
• weak discontinuity

In this paper, we investigate the behaviour of singularities and the formation of shocks for a class of multidimensional quasilinear hyperbolic systems of conservation laws including the multidimensional Keyfitz-Kranzer system with a radial state function. Precisely speaking, for these kind of systems we give sharp estimates on the blow-up rate of the smooth solution, provide a complete description of the solution close to the blow-up point, and construct the entropy solution in a neighbourhood of the blow-up point, which contains a unique shock surface issuing from the blow-up point.

• 出版日期2005-9-10
• 单位上海交通大学