發(fā)布時(shí)間：2018-05-28 22:27

  本文選題：分?jǐn)?shù)階Laplace算子 + 延拓　； 參考：《華東師范大學(xué)》2017年碩士論文

【摘要】：分?jǐn)?shù)階Laplace算子的定義比較復(fù)雜,為了方便讀者理解,文中我們?cè)敿?xì)給出了分?jǐn)?shù)階Laplace算子在Rn上的三種等價(jià)性定義以及在有界區(qū)域Ω上的兩種等價(jià)性定義.目前最常用的是Luis Caffarelli-Luis Silvestre的延拓性定義,用這種定義可以將非局部問題轉(zhuǎn)化為局部問題,使得我們可以用局部的方法去處理分?jǐn)?shù)階Laplace 算子.本文中我們考慮了分?jǐn)?shù)階擴(kuò)散方程其中(-△)αu(x)=Cn,αP.V.∫Rn((u(x)-u(y))/(|x-y|n+2α))dy是分?jǐn)?shù)階Laplace算子,α∈(0,1).利用它的基本解和壓縮映射原理,系統(tǒng)給出了方程解的存在性;并且我們研究了分?jǐn)?shù)階MEMS方程其中α ∈(0,1),λ＞ 0是一個(gè)常數(shù).根據(jù)λ的取值,給出了分?jǐn)?shù)階MEMS方程解的存在性.
[Abstract]:The definition of fractional order Laplace operator is complicated. In order to facilitate readers' understanding, we give three definitions of equivalence of fractional order Laplace operator on rn and two definitions of equivalence on bounded domain 惟. At present, the extension definition of Luis Caffarelli-Luis Silvestre is the most commonly used one. With this definition, the nonlocal problem can be transformed into a local problem, so that we can deal with fractional order Laplace operators in a local way. In this paper, we consider the fractional order diffusion equation in which ~ (-) 偽 u ~ n ~ (?) C _ n, 偽 P.V. ~ (?) ~ (-) ~ (?) By using its fundamental solution and contraction mapping principle, we give the existence of the solution of the equation, and we study the fractional order MEMS equation, where 偽 鈭，

本文編號(hào)：1948421