Pointwise Optimal Control for Diffusion Problems of Missing Data

The article concerns the mathematical analysis and optimal control for parabolic problems of pointwise source, where some boundary data are unknown. Precisely, pollution is located in a part of the boundary of the domain, and moreover, we suppose that one can act on the system only at some particula...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 14; no. 3; pp. 1 - 12
Main Authors Mahoui, S., Moulay, M. S., Omrane, A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2017
Springer Nature B.V
Subjects
Control systems
Lagoons
Mathematical analysis
Mathematics
Mathematics and Statistics
Missing data
Optimal control
Optimization
35K20
pointwise control
35K05
transposition method
missing data
low-regret control
singular optimality system
49K20
adjoint problem
Parabolic problems
93C20
93C41
49K35
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Summary:The article concerns the mathematical analysis and optimal control for parabolic problems of pointwise source, where some boundary data are unknown. Precisely, pollution is located in a part of the boundary of the domain, and moreover, we suppose that one can act on the system only at some particular points by a time-control function. The problem is common in the applications to pollution phenomena diffusing in a lagoon or an estuary. First, the existence and uniqueness of a solution to the original problem is proved using the transposition method. Then by applying the low-regret technique of J.-L. Lions, we show that the problem of optimal control admits a unique low-regret pointwise control that we characterize by a singular optimality system.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-017-0919-5