【摘要】：本文主要內(nèi)容分為兩部分,第一部分考慮具阻尼的Euler-Korteweg方程的解的漸近行為,得到當(dāng)時(shí)間充分大時(shí),方程的解收斂到非線性擴(kuò)散波,并得到相應(yīng)的收斂率;進(jìn)而證明當(dāng)Korteweg系數(shù)收斂于零時(shí),具阻尼Euler-Korteweg方程收斂于具阻尼的Euler方程.第二部分主要證明在一維空間中帶Korteweg項(xiàng)的兩相流模型的弱解的整體存在性.第一部分在證明過程中,通過具阻尼的Euler-Korteweg方程及Darcy定律的性質(zhì)得到校正函數(shù)的表達(dá)式,從而將具阻尼的Euler-Korteweg方程化簡(jiǎn)為一個(gè)新的方程,再通過構(gòu)造非線性擴(kuò)散方程的自相似解,得到非線性擴(kuò)散方程的解的耗散估計(jì),進(jìn)而將研究Euler-Korteweg方程收斂到非線性擴(kuò)散波的收斂估計(jì)轉(zhuǎn)化為研究新的方程收斂到零的衰減估計(jì).第二部分證明主要采用了能量估計(jì)的方法證明了帶Korteweg項(xiàng)的兩相流模型的弱解的整體存在性.
[Abstract]:The main content of this paper is divided into two parts. In the first part, the asymptotic behavior of the solution of the damped Euler-Korteweg equation is considered, and the solution of the equation converges to the nonlinear diffusion wave when the time is large enough, and the corresponding convergence rate is obtained, and then it is proved that when the Korteweg coefficient converges to 00:00, the damped Euler-Korteweg equation converges to the damped Euler equation. In the second part, we mainly prove the global existence of weak solutions of two-phase flow model with Korteweg term in one-dimensional space. In the first part, through the properties of damped Euler-Korteweg equation and Darcy law, the expression of correction function is obtained, and the damped Euler-Korteweg equation is reduced to a new equation, and then the dissipative estimation of the solution of nonlinear diffusion equation is obtained by constructing the self-similar solution of nonlinear diffusion equation. Furthermore, the convergence estimation of the Euler-Korteweg equation to the nonlinear diffusion wave is transformed into the attenuation estimation of the new equation converging to zero. In the second part, we prove the global existence of the weak solution of the two-phase flow model with Korteweg term by using the energy estimation method.
【學(xué)位授予單位】：華僑大學(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)：2510722