The study of an inverse problem for a fluid-solid interaction model in one-dimension

• Autores: Jone Apraiz Iza, Anna Doubova Krasotchenko , Enrique Fernández Cara , Masahiro Yamamoto
• Localización: FGS 2024 (French-German-Spanish Conference on Optimization) Proceedings: Proceedings / coord. por Rafael Gallego Amez , Mariano José Mateos Alberdi , 2024, ISBN 978-84-10135-30-7, págs. 17-22
• Idioma: español
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• Resumen

  • This article is a sample of what has been done in the research work [1] and has been presented in the French-German-Spanish Conference on Optimizaion 2024, that has been held in Gijón, Spain. In the work [1] we considered a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. There, we studied the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one end point of the spatial interval.

    In this article we display the main results we have obtained in [1] in order to establish uniqueness prop- erty and some conditional stability estimates. We also show a brief outline of the proofs, where we have used and adapted some lateral estimates that rely on appropriate Carleman and interpolation inequalities.