本文選題：歐拉方程組 + Chaplygin氣體��； 參考：《數學的實踐與認識》2017年11期

【摘要】：研究一維Chaplygin氣體歐拉方程組中波的相互作用.方程組的波包含接觸間斷和在密度變量以及內能變量上同時具有狄拉克函數的狄拉克激波.根據這些波的不同組合,問題被分成了7種情形.通過詳細地構造每種情形的整體解,獲得了各種波相互作用的完整結果.特別地,對于一類初值,兩個接觸間斷相互作用后,產生了一個狄拉克激波;然而,對于另外一類初值,一個狄拉克激波與一個接觸間斷相互作用后,狄拉克激波消失.這些都是波相互作用中非常特別的現象.
[Abstract]:The wave interaction in one dimensional Chaplygin gas Euler equations is studied. The waves of the equations contain contact discontinuities and Dirac shock waves with Dirac functions in both density and internal energy variables. According to the different combinations of these waves, the problem is divided into seven cases. By constructing the global solution of each case in detail, the complete results of various wave interactions are obtained. In particular, for one class of initial values, a Dirac shock wave is produced after two contact discontinuous interactions; however, for another initial value, a Dirac shock wave disappears after a Dirac shock wave interacts with a contact discontinuous interaction. These are very special phenomena in wave interaction.
【作者單位】： 貴州財經大學數統(tǒng)學院;
【基金】：國家自然科學基金(11661015,11526063) 貴州省科學技術基金(黔科合J字[2015]2026號) 貴州省教育廳自然科學研究項目(黔教合KY字[2015]482) 貴州省“千”層次創(chuàng)新人才項目
【分類號】：O175
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本文編號：1959664