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| ON INTERACTION OF SHOCK AND SOUND WAVE (II) |
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Citation： |
Chen Shuxing.ON INTERACTION OF SHOCK AND SOUND WAVE (II)[J].Chinese Annals of Mathematics B,1996,17(4):445~456 |
| Page view： 0
Net amount： 669 |
Authors： |
Chen Shuxing; |
Foundation： |
the National Natural ScienceFoundation of China and the Doctoral Programme Foundation of Institution High Education |
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| Abstract： |
This paper continues the discussion in [5], and proves the
existence of local solution to the problem of interaction of shock and gradient wave. The author uses Newton's iteration scheme to constructs a sequence of approximate solutions. By using delicate energy method the convergence of the sequence is
eatablished and then it leads to the existence of the genuine
solution. The main point of the energy method applied here is
first to estimate a linear combination of the approximate
solution and the function describing the characteristics of the
system, before estimating these two elements separately. The
method plays a key role, because it can aviod the smoothness loss caused by the characteristic boundary in the process of interation. |
Keywords： |
Shock wave, Sound wave, Nonlinear hyperbolic system, Asymptotic solution |
Classification： |
35L60, 76L05 |
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