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...

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Detalles Bibliográficos
Autores: Casas Rentería, Eduardo|||0000-0002-8364-9416, Kunisch, Karl, Tröltzsch, Fredi
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
Descripción
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.