- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 6 Issue: 4
- Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tik...
Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method
Authors : Ha Vo Thi Thanh, Ngo Hung, Nguyen Duc Phuong
Pages : 433-450
Doi:10.31197/atnaa.1079951
View : 6 | Download : 2
Publication Date : 2022-12-30
Article Type : Research
Abstract :In this paper, we study inverse source for diffusion equation with conformable derivative: $CoD_{t}^{(\\gamma)}u - \\Delta u = \\Phi(t) \\mathcal{F}(x)$, where $0<\\gamma<1,~ (x,t) \\in \\Omega \\times (0,T)$. 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