摘要
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.
基金
ProjectsupportedbytheNationalNaturalScienceFoundationofChinaandtheDoctoralProgrammeFoundationofInstitutionHighEducation
