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arXiv · 2003.00620

The stability for an inverse problem of bottom recovering in water-waves

R. Lecaros·J. López-Ríos·J. H. Ortega·S. Zamorano
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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.

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R. Lecaros, J. López-Ríos, J. H. Ortega, S. Zamorano. 2020-08-14. The stability for an inverse problem of bottom recovering in water-waves. https://doi.org/10.1088/1361-6420%2Fabafee

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