Inverse boundary value problem for the Convection-Diffusion equation with local data
Abstract
We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for the unique determination of the time-dependent convection and the density terms from the knowledge of the boundary data measured outside the inaccessible part. In the process, we show that there is a natural gauge in the perturbations, and we prove that this is the only obstruction in the uniqueness result.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.18361
- arXiv:
- arXiv:2407.18361
- Bibcode:
- 2024arXiv240718361K
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35R30;
- 35K20