Optimal control problem for an anisotropic parabolic problem in a domain with very rough boundary

In this paper, using Pontryagin’s maximum principle, we study the asymptotic behaviour of a parabolic optimal control problem in a domain Ω ε ⊂ R n , whose boundary ∂ Ω ε contains a highly oscillating part. On this part we consider a homogeneous Neumann boundary condition. We identify the limit prob...

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Bibliographic Details
Published inRicerche di matematica Vol. 63; no. 2; pp. 307 - 328
Main Authors De Maio, U., Faella, L., Perugia, C.
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 01.11.2014
Subjects
Algebra
Analysis
Geometry
Mathematics
Mathematics and Statistics
Numerical Analysis
Probability Theory and Stochastic Processes
Homogenization
35B27
35B37
49J20
Optimal control
Oscillating boundary
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Summary:In this paper, using Pontryagin’s maximum principle, we study the asymptotic behaviour of a parabolic optimal control problem in a domain Ω ε ⊂ R n , whose boundary ∂ Ω ε 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 ε -level.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-014-0183-y