A nonlinear fractional Rayleigh–Stokes equation under nonlocal integral conditions

Advances in Difference Equations

Van Thinh Nguyen¹  Nguyen Hoang Luc²  Le Dinh Long³  Ho Thi Kim Van³ 

[1] Department of Civil and Environmental Engineering, Seoul National University, Seoul, South Korea;Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam;Vietnam National University, Ho Chi Minh City, Vietnam;Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong Province, Vietnam;Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong Province, Vietnam;

关键词: Fractional Rayleigh–Stokes equation;    Ill-posed problem;    Regularization;    Existence;    Uniqueness;    Convergence estimation;   

DOI  :  10.1186/s13662-021-03545-z

来源: Springer

【 摘 要 】

In this paper, we study the fractional nonlinear Rayleigh–Stokes equation under nonlocal integral conditions, and the existence and uniqueness of the mild solution to our problem are considered. The ill-posedness of the mild solution to the problem recovering the initial value is also investigated. To tackle the ill-posedness, a regularized solution is constructed by the Fourier truncation method, and the convergence rate to the exact solution of this method is demonstrated.

【 授权许可】

CC BY