Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method

Authors : Ha VO THİ THANH, Ngo HUNG, Nguyen Duc PHUONG

Pages : 433-450

Doi:10.31197/atnaa.1079951

View : 9 | Download : 8

Publication Date : 2022-12-30

Article Type : Research Paper

Abstract :In this paper, we study inverse source for diffusion equation with conformable derivative: $CoD_{t}^{insert ignore into journalissuearticles values(\\gamma);}u - \\Delta u = \\Phiinsert ignore into journalissuearticles values(t); \\mathcal{F}insert ignore into journalissuearticles values(x);$, where $0<\\gamma<1,~ insert ignore into journalissuearticles values(x,t); \\in \\Omega \\times insert ignore into journalissuearticles values(0,T);$. We survey the following issues: The error estimate between the sought solution and the regularized solution under a priori parameter choice rule; The error estimate between the sought solution and the regularized solution under a posteriori \\\\ parameter choice rule; Regularization and ${\\mathscr L}_{p}$ estimate by Truncation method.
Keywords : inverse source problem, Fractional diffusion equation, Inverse problem, inverse source problem, Regularization