2022/03/22 by Xiangcheng Zheng, Zheng, Xiangcheng, Vincent J. Ervin +3
Mathematics · #33C45 #35B65 #41A10 #65N30 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2203.11705
openalex publication_date 2022/03/22 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper we investigate the variable coefficient two-sided fractional diffusion, advection, reaction equations on a bounded interval. It is known that the fractional diffusion operator may lose coercivity due to the variable coefficient, which makes both the mathematical and numerical analysis challenging. To resolve this issue, we design appropriate test and trial functions to prove the inf-sup condition of the variable coefficient fractional diffusion, advection, reaction operators in suitable function spaces. Based on this property, we prove the well-posedness and regularity of the solutions, as well as analyze the Petrov-Galerkin approximation scheme for the proposed model. Numerical experiments are presented to substantiate the theoretical findings and to compare the behaviors of different models.