Optimal control approach for moving bottom detection in one‐dimensional shallow waters by surface measurements
R. Lecaros,
J. López‐Ríos,
G. I. Montecinos
et al.
Abstract:We consider the Boussinesq‐Peregrine (BP) system as described by Lannes [Lannes, D. (2013). The water waves problem: mathematical analysis and asymptotics (Vol. 188). American Mathematical Soc.], within the shallow water regime, and study the inverse problem of determining the time and space variations of the channel bottom profile, from measurements of the wave profile and its velocity on the free surface. A well‐posedness result within a Sobolev framework for (BP), considering a time dependent bottom, is pre… Show more
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