简介：Thispaperstudiestheinteractionofshockandgradientwave(soundwave)ofsolutionstothesystemofinviscidisentropicgasdynamicsasamodelforthecorrespondingproblemsfornonlinearhyperbolicsystems.Theproblemcanbereducedtoaboundaryvalueprobleminawedgeddormain,ByusingthemethodofconstructingasymptoticsolutionsandNewton'siterationprocessitisprovedthatifaweakshockhitsagradientwave,thenthegrandientwavewillsplitintotwogradientwaves,whiletheshockcontinusespropagating.Inthispapertheauthorreducestheproblemtoastandardformandconstructsasymptoticsolutionoftheproblem.Theexistenceofthegenuinesolutionwillhegiveninthefollowingpaper.
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