| Abstract: |
| The direct problem of water-wave equations is the problem of determining the surface, and its velocity potential, in time $T>0$, for a given initial profile and velocity potential, where the profile of the bottom, the bathymetry, is known. In this talk, we present the inverse problem of recovering the shape of the solid bottom boundary of an inviscid, irrotational, incompressible fluid from measurements of a portion of the free surface. In particular, we will present some theoretical and numerical results for identifiability and numerical reconstruction of the bottom. |
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