希望在偏微分方程守恆律中，探討外力項對於齊次部份的影響，對時間及空間的變 化，觀察具體的管道流中包含了不規則管壁的摩擦係數和流體的熱傳導，合併Fanno 與 Rayleigh 模型中流體經過對稱不規則面積噴嘴的影響。推廣過去的Glimm 方法（GGS） 希望能提出了建立廣域解存在性以及對初始值小擾動下的穩定性探討，且此起始值條件 的能夠包含超音速與亞音速的狀態。致力於黎曼邊界值問題到邊界黎曼問題的波交互作 用，試著設計一個對於外力作用於齊次解的演化矩陣。估計其波相互作用後證明該解的 穩定性和存在性。更進一步，試著將此外力演化手法使用在數值方法上，來解讀其波交 互作用所產生之自然現象。 ;We concerned initial value or initial-boundary value problem of conservation laws. Studying the source term with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles. A new version of a generalized Glimm scheme (GGS) is presented for establishing the global existence of transonic entropy solutions. Modified Riemann and boundary Riemann solutions applied to design this GGS from the contraction matrices of the homogeneous Riemann (or boundary-Riemann) solutions. Moreover, extended Glimm-Goodman wave interaction estimates are investigated for ensuring the stability of the scheme and the positivity of gas velocity that leads to the existence of the weak solution. By showing the entropy inequality, we show that this weak solution is the entropy solution. Moreover, using numerical methods for approximating their solution for understanding wave-propagation phenomena.
