Artículo
Exact controllability to the trajectories of the one-phase Stefan problem
Autor/es | Bárcena Petisco, Jon Asier
Fernández Cara, Enrique Araujo de Souza, Diego |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2023-08-11 |
Fecha de depósito | 2024-01-30 |
Publicado en |
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Resumen | This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We ... This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Lyusternik-Graves' Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable. |
Cita | Bárcena Petisco, J.A., Fernández Cara, E. y Araujo de Souza, D. (2023). Exact controllability to the trajectories of the one-phase Stefan problem. Journal of Differential Equations, 376, 126-153. https://doi.org/10.1016/j.jde.2023.08.016. |
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