On a time fractional diffusion with nonlocal in time conditions

Advances in Difference Equations

Nguyen Hoang Luc¹  Nguyen Anh Triet¹  Nguyen Hoang Tuan²  Nguyen Duc Phuong³ 

[1] Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam;Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam;

关键词: Fractional diffusion equation;    Well-posed problem;    Ill-posed problem;    Regularization;    35R11;    35B65;    26A33;   

DOI  :  10.1186/s13662-021-03365-1

来源: Springer

【 摘 要 】

In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.

【 授权许可】

CC BY