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| ON INTERACTION OF SHOCK AND SOUND WAVE (I) |
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Citation： |
Chen Shuxing.ON INTERACTION OF SHOCK AND SOUND WAVE (I)[J].Chinese Annals of Mathematics B,1996,17(1):35~42 |
| Page view： 896
Net amount： 811 |
Authors： |
Chen Shuxing; |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
This paper studies the interaction of shock and gradient wave
(sound wave) of solutions to the system of inviscid isentropic
gas dynamics as a model for the corresponding problems for
nonlinear hyperbolic systems. The problem can be reduced to a
boundary value problem in a wedged domain. By using the method of
constructing asymptotic solutions and Newton's iteration process
it is proved that if a weak shock hits a gradient wave, then the
grandient wave will split into two gradient waves, while the
shock continuses propagating. In this paper the author reduces
the problem to a standard form and constructs asymptotic solution
of the problem. The existence of the genuine solution will be
given in the following paper. |
Keywords： |
Shock wave, Sound wave, Nonliner hyperbolic
system, Asymptotic solution |
Classification： |
35L60, 76L05 |
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