Inverse Problems for One-Dimensional Fluid-Solid Interaction Models

doi:10.1007/s42967-024-00437-3

Communications on Applied Mathematics and Computation ›› 2026, Vol. 8 ›› Issue (1): 309-323.doi: 10.1007/s42967-024-00437-3

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Inverse Problems for One-Dimensional Fluid-Solid Interaction Models

J. Apraiz¹, A. Doubova², E. Fernández-Cara², M. Yamamoto³

1. Dpto. Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Barrio Sarriena s/n, 48940, Leioa, Bizkaia, Spain;
2. Dpto. EDAN e IMUS, Universidad de Sevilla, Campus Reina Mercedes, 41012, Seville, Spain;
3. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan

Received:2024-01-31 Revised:2024-05-06 Online:2026-02-20 Published:2026-02-11
Contact: J. Apraiz,E-mail:jone.apraiz@ehu.eus E-mail:jone.apraiz@ehu.eus
Supported by:
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.

Abstract

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.

Key words: Burgers equation, Fluid-solid interaction, Free boundaries, Inverse problems, Stability, Uniqueness

CLC Number:

J. Apraiz, A. Doubova, E. Fernández-Cara, M. Yamamoto. Inverse Problems for One-Dimensional Fluid-Solid Interaction Models[J]. Communications on Applied Mathematics and Computation, 2026, 8(1): 309-323.

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Inverse Problems for One-Dimensional Fluid-Solid Interaction Models

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