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Optimal control problems with final observation governed by explosive parabolic equations


Amann, H; Quittner, P (2005). Optimal control problems with final observation governed by explosive parabolic equations. SIAM Journal on Control and Optimization, 44(4):1215-1238.

Abstract

We study optimal control problems with final observation. The governing parabolic equations or systems involve superlinear nonlinearities, and their solutions may blow up in finite time. Our proof of the existence, regularity, and optimality conditions for an optimal pair is based on uniform a priori estimates for the approximating solutions. Our conditions on the growth of the nonlinearity are essentially optimal. In particular, we also solve a long-standing open problem of Lions concerning singular systems.
©2005 Society for Industrial and Applied Mathematics

Abstract

We study optimal control problems with final observation. The governing parabolic equations or systems involve superlinear nonlinearities, and their solutions may blow up in finite time. Our proof of the existence, regularity, and optimality conditions for an optimal pair is based on uniform a priori estimates for the approximating solutions. Our conditions on the growth of the nonlinearity are essentially optimal. In particular, we also solve a long-standing open problem of Lions concerning singular systems.
©2005 Society for Industrial and Applied Mathematics

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:optimal control problem, nonlinear parabolic equation, blow-up, final observation, optimality conditions, strong nonlinearities
Language:English
Date:2005
Deposited On:01 Feb 2010 07:51
Last Modified:19 Feb 2018 19:57
Publisher:Society for Industrial and Applied Mathematics
ISSN:0363-0129
Additional Information:Copyright © 2005, Society for Industrial and Applied Mathematics
OA Status:Green
Publisher DOI:https://doi.org/10.1137/S0363012903433450

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