Propagation of viscous shock waves away from the boundary

Chiu Ya Lan, Huey E.R. Lin, Tai Ping Liu, Shih Hsien Yu

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

We study the propagation of shock waves away from the boundary for viscous conservation law. Our main purpose is to obtain pointwise description of the perturbation of the shock profile. We show that there are different convergence rates for the region between the boundary and the shock and the region ahead of the shock. The dependence of these rates on the shock strength, viscosity, and initial perturbation is studied. There are two mechanisms which govern the solution behavior: the compressibility of the shock and the presence of the boundary. We introduce an iteration scheme to decouple these two effects. Thus near the boundary we use the Green's function for the initial-boundary value problem of the equation linearized around the boundary value; away from the boundary we use the Green's function for the initial-value problem of the equation linearized around the shock profile. To focus on our main ideas, we study the Burgers equation, for which the Green's functions have explicit forms. Our new approach should be applicable to more general situations such as the system of viscous conservation laws.

原文英語
頁(從 - 到)580-617
頁數38
期刊SIAM Journal on Mathematical Analysis
36
發行號2
DOIs
出版狀態已發佈 - 2005 三月 29

ASJC Scopus subject areas

  • 分析
  • 計算數學
  • 應用數學

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