Date: Fri. July 4, 2025
Event: DeustoCCM Seminar
Session 01 (11:30H)
Title: Lipschitz stability in inverse problems for semi-discrete parabolic operators
Speaker: Prof. Rodrigo Lecarós
Affiliation: Universidad Técnica Federico Santa María, Chile
Abstract. This presentation will address an inverse problem for a semi-discrete parabolic equation, where the objective is to identify the term on the right-hand side of the equation (the source) from measurements of the solution at an intermediate time and within a spatial subdomain. From this result, a stability estimate can be established for the potential function when it depends solely on space.
A new Carleman estimate will be presented in the semi-discrete context, whose parameter dependence is determined by the mesh size. Furthermore, it will analyze how the discrete terms arising in the Carleman inequality introduce an error term associated with the initial condition of the solution in the semi-discrete system.
Session 02 (12:30H)
Title: On the controllability of the water-waves equation in bounded domains
Speaker: Prof. Juan Carlos López Ríos
Affiliation: Universidad Industrial de Santander, Colombia
Abstract. We present the mathematical problem of controlling the waves in a domain, by injecting fluid jets through the walls; in the context of gravity waves (incompressible, non-viscous fluids). Using conformal mappings and the Dirichlet-Neumann operator, the problem is formulated as a second order evolutionary equation on the free surface, involving a nonlocal, self adjoint operator. We develop the appropriate functional framework to have solutions and study exact and approximate controllability through observability and a unique continuation principle. The results are based on works published in [1] and [2].
References
[1] M. A. Fontelos, R. Lecaros, J. López-Ríos, and A. Pérez. On the unique continuation property for the two-dimensional sloshing problem. Z. Angew. Math. Phys., Accepted, 2025.
[2] M. A. Fontelos and J. López-Ríos. Controllability of surface gravity waves and the sloshing problem. ESAIM Control Optim. Calc. Var., 29:Paper No. 65, 29, 2023.
WHERE
University of Deusto, DeustoTech.
Room: Logistar
Unibertsitate Etorb., 24, 48007 Bilbo, Bizkaia
