Determine source of Cahn–Hilliard equation with time‐fractional derivative by iterative variational regularization method
Jing Li, Hao Cheng · Mathematical Methods in the Applied Sciences · 2023
In this paper, we consider the inverse problem for the time‐fractional two‐dimensional Cahn–Hilliard equation. The ill‐posedness and a conditional stability of the inverse problem are proved. We present a new iterative variational regularization method to solve it. The convergence rates of the regularized solutions under the a priori regularization parameter choice rule and a posteriori regularization parameter choice rule are obtained. Numerical examples illustrate the effectiveness and stability of our proposed method.