Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion
Abstract
Abstract. In this work, we investigate the unique identifiability and stable recovery of a spatially dependent variable-order in the subdiffusion model from the boundary flux measurement. We establish several new unique identifiability results from the observation at one point on the boundary without / with the knowledge of medium properties and a conditional Lipschitz stability estimate when the observation is available on the whole boundary. The analysis crucially employs resolvent estimates in the [Formula: see text] ([Formula: see text]) spaces, solution representation in the Laplace domain, and novel asymptotic expansions of the Laplace transform of the boundary flux at [Formula: see text] and [Formula: see text].
Fields of Study & Subjects
Model Reduction and Neural Networks
Numerical methods in engineering
Nonlinear Waves and Solitons
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 1
- Pages
- 238–259
- Publication date
- 8 January 2026
- Language
- EN