On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients
Analysis of PDEs
2022-08-11 v1
Abstract
We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the Dirichlet-to-Neumann map. We exploit the integration by parts formula for Riemann-Liouville and Caputo derivatives to derive the Runge approximation property for our space-time fractional operator based on the unique continuation property of the fractional Laplacian. This enables us to extend early unique determination results for space-fractional but time-local operators to the space-time fractional case.
Keywords
Cite
@article{arxiv.2208.05012,
title = {On inverse problems for uncoupled space-time fractional operators involving time-dependent coefficients},
author = {Li Li},
journal= {arXiv preprint arXiv:2208.05012},
year = {2022}
}