Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 14 de diciembre de 2022
Hora  : 11:30
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Raul Kazan da Cunha Araújo

(Posdoctoral en el Institut de Mathématiques de Bordeau)

Resumen

This talk concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting processes. In each phase, a parabolic equation, completed with initial and boundary conditions must be satisfied; the phases are separated by a phase-change interface where an additional free-boundary condition is imposed. We assume that two localized sources of heating/cooling controls act on the system (one in each phase). We prove a local null controllability result: the temperatures and the interface can be respectively steered to zero and to a prescribed location provided the initial data and interface position are sufficiently close to the targets. The ingredients of the proofs are a compactness-uniqueness argument and a fixed-point formulation and resolution of the controllability problem (to deduce the result for the nonlinear system). We also prove a negative result corresponding to the case where only one control acts on the system and the interface does not collapse to the boundary.