A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation

By Ting Wei, Jun-Gang Wang. 2014

172 citations recorded by the source corpus.

In this paper, we consider an inverse source problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine a space-dependent source term in the time-fractional diffusion equation from a noisy final data. Based on a series expression of the solution, we can transform the original inverse problem into a first kind integral equation. The uniqueness and a conditional stability for the space-dependent source term can be obtained. Further, we propose a modified quasi-boundary value regularization method to deal with the inverse source problem and obtain two kinds of convergence rates by using an a priori and an a posteriori regularization parameter choice rule, respectively. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.

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

View Paper: https://www.semanticscholar.org/paper/291f532f0a78cea1ac352790deea02f3b9d45c57

Citations in the corpus

• An inverse time-dependent source problem for a time-fractional diffusion equation (2016, unknown): “Wei and Wang in [36, 37] solved a backward problem and an inverse space-dependent source problem by a modified quasi-boundary value method.”
• A tutorial on inverse problems for anomalous diffusion processes (2015, unknown): “In [101], the numerical recovery of a spatially varying function of the source term from the final time data in a general domain was studied using a quasi-boundary value problem method; see also [112, 98] related studies.”