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

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.

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.