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.
Authors
- Anna Doubova (ORCID: https://orcid.org/0000-0002-5708-2700)
- Jone Apraiz (ORCID: https://orcid.org/0000-0001-7866-8412)
- Masahiro Yamamoto (ORCID: https://orcid.org/0000-0002-4050-871X)
- Enrique Fernández‐Cara (ORCID: https://orcid.org/0000-0001-6293-9249)
Institutions
- University of the Basque Country (ES)
- Instituto de Recursos Naturales y Agrobiología de Sevilla (ES)
- The University of Tokyo (JP)
- Universidad de Sevilla (ES)
Publication Details
- Journal
- Communications on Applied Mathematics and Computation
- Published
- 2024-09-10
- DOI
- https://doi.org/10.1007/s42967-024-00437-3
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministerio de Ciencia, Innovación y Universidades
- Hezkuntza, Hizkuntza Politika Eta Kultura Saila, Eusko Jaurlaritza
- Eusko Jaurlaritza
- Ministerio de Ciencia e Innovación
- Japan Society for the Promotion of Science
- European Regional Development Fund
- Agencia Estatal de Investigación