About the convergence of a family of initial boundary value problems for a fractional diffusion equation of robin type
作者：
Highlights：
• We work with a fractional diffusion equation (FDE) where the fractional derivative is the Caputo derivative in time of order α∈(0,1).
• The governing equation models subdiffusion proccesses.
• We prove the existence of SOLA solution to an initial-boundary value problem of Robin type, governed by the FDE.
• We use a Fourier approach for the whole problem and variational techniques for dealing with the problems related to the spatial variable.
• We have special interest in the coefficient β, which is the Newton coefficient of heat transfer, and we consider it increasing to infinity.
• With the help of the results on eigenvalues and eigenfunctions given in a recent work of Filinovsky (Mathematica Boemica 139(2014): 341–352), we prove that the family of solutions of the Robin type problems (with parameter β), converges to the solution given by Sakamoto and Yamamoto in 2011 (J. Math. Anal. Appl. 382(2011):426-447) for an analogous problem of Dirichlet type.
摘要
•We work with a fractional diffusion equation (FDE) where the fractional derivative is the Caputo derivative in time of order α∈(0,1).•The governing equation models subdiffusion proccesses.•We prove the existence of SOLA solution to an initial-boundary value problem of Robin type, governed by the FDE.•We use a Fourier approach for the whole problem and variational techniques for dealing with the problems related to the spatial variable.•We have special interest in the coefficient β, which is the Newton coefficient of heat transfer, and we consider it increasing to infinity.•With the help of the results on eigenvalues and eigenfunctions given in a recent work of Filinovsky (Mathematica Boemica 139(2014): 341–352), we prove that the family of solutions of the Robin type problems (with parameter β), converges to the solution given by Sakamoto and Yamamoto in 2011 (J. Math. Anal. Appl. 382(2011):426-447) for an analogous problem of Dirichlet type.
论文关键词：Fractional diffusion equation,Robin condition,Fourier approach,Asymptotic behavior,SOLA solutions
论文评审过程：Received 22 May 2021, Revised 1 July 2022, Accepted 2 July 2022, Available online 21 July 2022, Version of Record 21 July 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127375
