| ON INTERACTION OF SHOCK AND SOUND WAVE （II） |
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| 作者姓名： | Chen Shuxing |
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| 作者单位： | Chen Shuxing * *Institute of Mathematics，Fudan University，Shanghai 200433，China. |
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| 基金项目： | ProjectsupportedbytheNationalNaturalScienceFoundationofChinaandtheDoctoralProgrammeFoundationofInstitutionHighEducation |
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| 摘 要： | Ｉｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｔｉｎｕｅｏｕｒｄｉｓｃｕｓｓｉｏｎｉｎ5].Ｍａｉｎｌｙｗｅｗｉｌｌｅｓｔａｂｌｉｓｈａｐｒｉｏｒｉｅｓｔｉｍａｔｅｓｆｏｒｔｈｅｌｉｎｅａｒｉｚｅｄｐｒｏｂｌｅｍ(Ｇ),ａｎｄｔｈｅｎｐｒｏｖｅｔｈｅｅｘｉｓｔｅｎｃｅｏｆｔｈｅｓｏｌｕｔｉｏｎｔｏｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍ.Ｉｎ§5ｗｅｇｉｖｅｓｏｍｅｔｅｃｈｎｉｃａｌｐｒｅｐａｒａｔｉｏｎｓ.Ｔｈｅｎｔｈｅｗｈｏｌｅ§6ｉｓｄｅｖｏｔｅｄｔｏｔｈｅｅｓｔａｂｌｉｓｈｍｅｎｔｏｆｅｎｅｒｇｙｅｓｔｉｍａｔｅｓ.Ｉ…
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| 关 键 词： | 声波 振动波 双曲线系 渐进解 |
| 收稿时间： | 4/5/1994 12:00:00 AM |
| 修稿时间： | 1995/1/19 0:00:00 |
ON INTERACTION OF SHOCK AND SOUND WAVE (II) |
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| Chen Shuxing.ON INTERACTION OF SHOCK AND SOUND WAVE (II)[J].Chinese Annals of Mathematics,Series B,1996,17(4):445-456. |
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| Authors: | Chen Shuxing |
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| Institution: | InstituteofMathematics,FudanUniversity,Shanghai200433,China. |
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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. |
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| Keywords: | Shock wave Sound wave Nonlinear hyperbolic system Asymptotic solution |
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