1. The stability for an inverse problem of bottom recovering in water-waves
- Author
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Lecaros, R., López-Ríos, J., Ortega, J. H., and Zamorano, S.
- Subjects
Mathematics - Analysis of PDEs - Abstract
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water--waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation., Comment: version 2
- Published
- 2020
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