Inverse Problems for One-Dimensional Fluid-Solid Interaction Models

Abstract

We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one endpoint of the spatial interval. In particular, we establish unique results and some conditional stability estimates. For the proofs, we use and adapt some lateral estimates that, in turn, rely on appropriate Carleman and interpolation inequalities.

Keywords

Burgers equation / Fluid-solid interaction / Free boundaries / Inverse problems / Stability / Uniqueness / 35K15 / 35R35 / 35R30 / 35B35 / 65M32

References

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Funding

Ministerio de Ciencia, Innovación y Universidades(PID2021-126813NB-I00)

Hezkuntza, Hizkuntza Politika Eta Kultura Saila, Eusko Jaurlaritza(IT1615-22)

Japan Society for the Promotion of Science((A) 20H00117)

RIGHTS & PERMISSIONS

The Author(s)