本文關(guān)鍵詞：P-方程組活塞問(wèn)題大疏散波的存在性　出處：《華東師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： p-方程組 活塞問(wèn)題 間斷追蹤 修正的Glimm泛函 近似解 大疏散波

【摘要】：有一個(gè)水平放置無(wú)限長(zhǎng)的均勻截面的細(xì)長(zhǎng)管,管內(nèi)充滿了靜止氣體,中間有活塞.當(dāng)活塞以一定速度向左運(yùn)動(dòng)時(shí),活塞的運(yùn)動(dòng)必然導(dǎo)致細(xì)長(zhǎng)管內(nèi)氣體的運(yùn)動(dòng).當(dāng)氣體初始狀態(tài)和活塞運(yùn)動(dòng)速度滿足適當(dāng)條件時(shí),我們用間斷追蹤法證明了 P-方程組的初邊值問(wèn)題描述的該活塞問(wèn)題有包含大疏散波的整體解.本文的主要內(nèi)容包括:將問(wèn)題轉(zhuǎn)化到拉格朗日坐標(biāo)下;通過(guò)隱函數(shù)定理證明各種黎曼問(wèn)題的可解性;求解各種典型的黎曼問(wèn)題得到波之間的相互作用估計(jì);選擇恰當(dāng)?shù)臋?quán)構(gòu)造Glimm泛函得到Glimm泛函的遞減性.本文為了處理弱波與大疏散波的相互作用,對(duì)Glimm泛函作出適當(dāng)?shù)男拚?
[Abstract]:There is a slender tube with an infinitely long uniform section horizontally filled with static gas and a piston in the middle. When the piston moves to the left at a certain speed. The movement of the piston will inevitably lead to the movement of the gas in the slender tube. When the initial state of the gas and the velocity of the piston motion meet the appropriate conditions. By using the discontinuous tracing method, we prove that the piston problem described by the initial-boundary value problem of the P- equations has a global solution containing large evacuation waves. The main contents of this paper are as follows: transform the problem to Lagrange coordinates; The solvability of various Riemannian problems is proved by implicit function theorem. Some typical Riemannian problems are solved to estimate the interaction between waves. In order to deal with the interaction between weak wave and large evacuation wave, the Glimm functional is modified appropriately in this paper.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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本文編號(hào)：1363290