福州大学学报(自然科学版)
福州大學學報(自然科學版)
복주대학학보(자연과학판)
JOURNAL OF FUZHOU UNIVERSITY(NATURAL SCIENCE EDITION)
2015年
4期
435-439
,共5页
分数阶导数%弱解%变分形式%适定性
分數階導數%弱解%變分形式%適定性
분수계도수%약해%변분형식%괄정성
fractional derivative%weak solution%variation formulation%well-posedness
研究一类二维分数阶偏微分方程的边值问题,主要包括两方面内容:一是研究了合适的分数阶Sobolev空间及分数阶算子的性质;二是发展了一个弱解的理论框架,并建立了弱解的适定性理论。这是构造数值方法(如有限元和谱方法等)求解二维分数阶偏微分方程的理论基础。
研究一類二維分數階偏微分方程的邊值問題,主要包括兩方麵內容:一是研究瞭閤適的分數階Sobolev空間及分數階算子的性質;二是髮展瞭一箇弱解的理論框架,併建立瞭弱解的適定性理論。這是構造數值方法(如有限元和譜方法等)求解二維分數階偏微分方程的理論基礎。
연구일류이유분수계편미분방정적변치문제,주요포괄량방면내용:일시연구료합괄적분수계Sobolev공간급분수계산자적성질;이시발전료일개약해적이론광가,병건립료약해적괄정성이론。저시구조수치방법(여유한원화보방법등)구해이유분수계편미분방정적이론기출。
We investigate the boundary value problem of two-dimensional fractional partial differenti-al equations ( FEPDEs) .The main contributions of this work are twofold:first, we investigate suitable fractional Sobolev spaces for fractional partial differential equations and study the properties of the frac-tional operator.Then, we develop a theoretical framework of weak solutions and establish the well-posedness of the weak solutions.Consequently, this work provides the theory for constructing numeri-cal method such as finite element method and spectral method for solving the fractional partial differen-tial equations.