Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Professor Aiguo Xiao, Xiangtan University
Inviter:	Professor Yifa Tang
Title:	Space-Fractional Diffusion Equation with Variable Coefficients: Well-posedness and Fourier Pseudospectral Approximation
Language:	Chinese
Time & Venue:	2023.09.09 09:30-10:30 N702
Abstract:	Multi-dimensional space-fractional diffusion equation with variable coefficients and fractional gradient is a difficult problem in theory and computation. As far as we know, there rarely exist well-posedness results and efficient numerical approaches for such equation. In this talk, we focus on this subject. First, we apply the commutator estimation method to prove the coercivity of the non-positive bilinear form for such equation in both continuous and discrete senses, and this is key for the later discussion. Then, we prove the well-posedness of the analytical solution and give the global error estimation of the numerical solution obtained by Crank-Nicolson Fourier pseudospectral scheme. Last, the numerical experiments are used to verify the main results of the theoretical analysis, and a model for the plume of solute through groundwater is exhibited to show the application of space-fractional diffusion theory.