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

Yıl 2022, Cilt: 6 Sayı: 4, 433 - 450, 30.12.2022

Ha Vo Thi Thanh Ngo Hung Nguyen Duc Phuong

https://doi.org/10.31197/atnaa.1079951

Öz

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.

Anahtar Kelimeler

inverse source problem, Fractional diffusion equation, Inverse problem, inverse source problem, Regularization

Destekleyen Kurum

Industrial University of Ho Chi Minh City, Vietnam under Grant named “Investigate some fractional partial differential equations”

Proje Numarası

Grant No. 21/1CB03

Kaynakça

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