文章摘要
引用本文:苏延辉.一类二维分数阶偏微分方程解的适定性[J].福州大学学报(自然科学版),2015,43(4):435~439
一类二维分数阶偏微分方程解的适定性
Well-posedness of the 2D-fractional partial differential equations
  
DOI:10.7631/issn.1000-2243.2015.04.0435
中文关键词: 分数阶导数  弱解  变分形式  适定性
英文关键词: fractional derivative  weak solution  variation formulation  well-posedness
基金项目:
作者单位
苏延辉 福州大学数学与计算机科学学院福建 福州 350116 
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中文摘要:
      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.
英文摘要:
      We investigate the boundary value problem of two-dimensional fractional partial differential 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 fractional 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 numerical method such as finite element method and spectral method for solving the fractional partial differential equations.
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