In this paper, using Pontryagin's maximum principle, we study the asymptotic behaviour of a parabolic optimal control problem in a domain $\Omega _{\varepsilon}\subset\mathbf{R}^{n},$ whose boundary $\partial\Omega _{\varepsilon}$ contains a highly oscillating part. On this part we consider a homogeneous Neumann boundary condition. We identify the limit problem, which is an optimal control problem for the limit equation. Moreover, we explicitly remark that both limit state equation and limit cost are different from those ones at $\varepsilon-$level.
Optimal Control Problem for an Anisotropic Parabolic Problem in a Domain with Very Rough Boundary / DE MAIO, Umberto; L., Faella; C., Perugia. - In: RICERCHE DI MATEMATICA. - ISSN 1827-3491. - 63:2(2014), pp. 307-328. [10.1007/s11587-014-0183-y]
Optimal Control Problem for an Anisotropic Parabolic Problem in a Domain with Very Rough Boundary
DE MAIO, UMBERTO;
2014
Abstract
In this paper, using Pontryagin's maximum principle, we study the asymptotic behaviour of a parabolic optimal control problem in a domain $\Omega _{\varepsilon}\subset\mathbf{R}^{n},$ whose boundary $\partial\Omega _{\varepsilon}$ contains a highly oscillating part. On this part we consider a homogeneous Neumann boundary condition. We identify the limit problem, which is an optimal control problem for the limit equation. Moreover, we explicitly remark that both limit state equation and limit cost are different from those ones at $\varepsilon-$level.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
