| Abstract: |
| In this talk, we will address the inverse problem of recovering a degeneracy region within the diffusion coefficient of a parabolic equation by observing the normal derivative at the boundary. The strongly degenerate case is analyzed and our method is based on a careful analysis of the spectral problem. In particular, we derive sufficient conditions on the initial data that guarantee stability and uniqueness of the solution obtained from a one-point measurement. Moreover, we present more general uniqueness theorems, which also cover the identification of the initial data and the degeneracy power, using measurements taken over time.
Our investigations cover the case of real 1-D degenerate parabolic systems of equations with a specific coupling. Besides, possible extensions to multidimensional parabolic equations will be also analyzed. Theoretical results are also supported by numerical simulations. This talk is based on works in collaboration with P. Cannarsa and A. Doubova. |
|