On the value function for optimal control of semilinear parabolic equations
The value function for an infinite horizon tracking type optimal control problem with semilinear parabolic equation is investigated. In view of a possible nonconvexity of the optimal control problem, a local version of the value function is considered. Its differentiability is proved for initial dat...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/39167 |
| Acceso en línea: | https://hdl.handle.net/10902/39167 |
| Access Level: | acceso abierto |
| Palabra clave: | Semilinear parabolic equation Infinite time horizon Optimal control Local value function Second order optimality conditions Hamilton-Jacobi-Bellman equation |
| Sumario: | The value function for an infinite horizon tracking type optimal control problem with semilinear parabolic equation is investigated. In view of a possible nonconvexity of the optimal control problem, a local version of the value function is considered. Its differentiability is proved for initial data in a neighborhood around the nominal initial value, provided a second order sufficient optimality condition is fulfilled for the nominal locally optimal control. Based on the differentiability of the value function, a Hamilton-Jacobi-Bellman equation is derived. |
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