本文關(guān)鍵詞： 非局部 有界區(qū)域 廣義Burgers方程 Ginzburg-Landau方程 白噪聲 鞅解　出處：《四川師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：Burgers方程和Ginzburg-Landau方程由于分別模擬了沖擊波的傳播和超導(dǎo)現(xiàn)象而受到物理學(xué)家和數(shù)學(xué)家的關(guān)注.本文主要對有界區(qū)域上的隨機非局部廣義Burgers方程和Ginzburg-Landau方程感興趣,證明了其鞅解的存在性.第一章介紹了 Burgers方程和Ginzburg-Landau方程的物理背景和已有研究,列出了文章所需的定義、不等式及引理,并給出了論文的主要結(jié)論.第二章研究了有界區(qū)域上的隨機非局部廣義Burgers方程.首先通過在適當(dāng)?shù)姆謹(jǐn)?shù)階加權(quán)Sobolev空間上考慮,克服了有界區(qū)域上非局部Laplace算子帶來的困難,然后通過Galerkin近似、Prokhorov定理、Skorokhod定理以及鞅表示定理獲得了系統(tǒng)鞅解的存在性.第三章利用類似的方法證明了有界區(qū)域上的隨機非局部Ginzburg-Landau方程鞅解的存在性.最后一章對以后的研究工作進行思考和展望.
[Abstract]:The Burgers and Ginzburg-Landau equations by physicists and mathematicians concerned because of the shock wave propagation and superconductivity were simulated. This paper focuses on the random non local generalized Burgers equation and the Ginzburg-Landau equation in bounded domain of interest, prove the existence of solutions of the martingale. The first chapter introduces the physical background and the existing research of Burgers equation and the Ginzburg-Landau equation, a list of the definitions required, inequality and lemma, and gives the main conclusions of the thesis. The second chapter studies the random non local generalized Burgers equation in bounded domain. Firstly, by considering the fractional order weighted Sobolev space properly, overcomes the difficulties of non local operators bring Laplace bounded domain, then by Galerkin approximation, Prokhorov theorem, Skorokhod theorem and martingale representation theorem to obtain the existence of solutions for the system of martingale. In the three chapter, we prove the existence of martingale solutions for stochastic nonlocal Ginzburg-Landau equations on bounded domains by using similar methods. In the last chapter, we consider and prospect future research.

【學(xué)位授予單位】：四川師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.2

【參考文獻】

相關(guān)期刊論文 前1條

1 何興;陳光淦;楊歡;;有界區(qū)間上的隨機廣義非局部Burgers方程鞅解的存在性[J];四川師范大學(xué)學(xué)報(自然科學(xué)版);2016年06期

，

本文編號：1444455