Inverse source problem for a fractional diffusion equation

By Ying Zhang, Xiang Xu. 2011

296 citations recorded by the source corpus.

Subfields: Mathematical Physics, Mechanics of Materials, Modeling and Simulation

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. 许传炬
2. Ngartelbaye Guerngar
3. Mohammad F. Al-Jamal
4. G. Em Karniadakis
5. Lu Lu
6. Suleyman Ulusoy
7. Mokhtar Kirane
8. Chuanju Xu

In Mechanics of Materials

1. Lu Lu
2. 许传炬
3. Mohammad F. Al-Jamal
4. G. Em Karniadakis
5. Suleyman Ulusoy
6. Chuanju Xu
7. Guofei Pang
8. X. Ye

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. 许传炬
4. Suleyman Ulusoy
5. X. Ye
6. Guofei Pang
7. Chuanju Xu
8. Mohammad F. Al-Jamal

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “For inverse problems, little is known about 3D space-time-fractional ADEs with a fractional Laplacian, despite some existing works on 1D and 2D problems [41, 42, 43, 44, 45, 46].”
• An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions (2013, background): “In [7], the inverse problem of determining the source term (which is independent of the time variable) for the fractional diffusion equation is considered.”
• A tutorial on inverse problems for anomalous diffusion processes (2015, unknown): “Zhang and Xu [111] established the unique recovery of a space dependent source term in (3.”
• A backward problem for the time‐fractional diffusion equation (2017, background): “Zhang and Xu [18] considered the problem of identifying the time-independent source term f from the boundary data u.”
• Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization (2017, background): “Recent efforts for fractional order identification have mainly focused on time-fractional advectiondespersion equations (ADEs) [4, 5, 6, 7, 8, 9] and, to a lesser extent, on parameter identification of the space-fractional ADEs but only limited to constant fractional order [10, 11, 12].”
• Inverse problem for a three-parameter space-time fractional diffusion equation (2018, background): “While most of these works have been dedicated to fractional derivatives only in the time variable [3, 10, 13, 14, 17, 18, 22, 23, 24], space-time fractional derivatives were considered in [20, 21], similarly as in this article.”
• A UNIQUENESS RESULT FOR AN INVERSE PROBLEM IN A SPACE-TIME FRACTIONAL DIFFUSION EQUATION (2013, background): “Important references documenting the recent interest on inverse problems with fractional derivatives are [4, 6, 9, 10, 13, 14, 16, 17, 18].”
• Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, methodology): “Unlike the work [21], which uses the eigenfunction expansion of the solution as the main tool, we will adapt the optimal control framework [10] to treat the inverse problem.”