Stackelberg-Nash controllability for a multi-objective Stefan problem
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917454101348352 |
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| author | de Carvalho, Thiago C. A Silva, Suerlan de Sousa-Neto, Gilcenio R. Vieira, Franciane de B. |
| author_facet | de Carvalho, Thiago C. A Silva, Suerlan de Sousa-Neto, Gilcenio R. Vieira, Franciane de B. |
| contents | We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective free-boundary problem. The interaction between the hierarchical control and the moving interface results in a nonlinear optimality system, and we show that the original problem reduces to the null controllability of this optimality system. Under suitable geometric conditions on the control regions, we establish a local null controllability result. The proof relies on an observability inequality for a linearized system, obtained through Carleman estimates adapted to the presence of a moving boundary. These results constitute, to the best of our knowledge, the first treatment of a Stefan system within a Stackelberg-Nash framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00999 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stackelberg-Nash controllability for a multi-objective Stefan problem de Carvalho, Thiago C. A Silva, Suerlan de Sousa-Neto, Gilcenio R. Vieira, Franciane de B. Optimization and Control Analysis of PDEs We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective free-boundary problem. The interaction between the hierarchical control and the moving interface results in a nonlinear optimality system, and we show that the original problem reduces to the null controllability of this optimality system. Under suitable geometric conditions on the control regions, we establish a local null controllability result. The proof relies on an observability inequality for a linearized system, obtained through Carleman estimates adapted to the presence of a moving boundary. These results constitute, to the best of our knowledge, the first treatment of a Stefan system within a Stackelberg-Nash framework. |
| title | Stackelberg-Nash controllability for a multi-objective Stefan problem |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2605.00999 |