Pontryagin's maximum principle of optimal control governed by some non-well-posed semilinear parabolic differential equations
type: Item
instance of: scholarly article
title: Pontryagin's maximum principle of optimal control governed by some non-well-posed semilinear parabolic differential equations
zbMATH Open document ID: 1019.49025
DOI: 10.1016/S0362-546X(02)00141-4
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-05-04T00:00:00Z
review text: The systems are of the form \[ {\partial y(t, x) \over \partial t} = Ay(t, x) + f(t, x, y(t, x), u(t, x)) \quad (0 < t \leq T, x \in \Omega) \tag{1} \] with \(A\) a uniformly elliptic operator in an \(n\)-dimensional domain \(\Omega\) and the Dirichlet boundary condition on \(\Gamma =\) boundary of \(\Omega.\) It is not assumed that (1) has the global existence property, and the optimal problems involve minimization of an integral functional under control constraints and a two point state constraint. The results in this paper are versions of Pontryagin's maximum principle. For systems of similar type where the control appears linearly, see [\textit{G. Wang} and \textit{L. Wang}, SIAM J. Control Optimization 40, 1517-1539 (2002; Zbl 1013.49016)].
reviewed by: Hector O. Fattorini
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R25
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1903493
zbMATH Keywords: non well-posed semilinear parabolic equations
zbMATH Keywords: local existence
zbMATH Keywords: optimal control
zbMATH Keywords: Pontryagin's maximum principle
author: Gengsheng Wang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1903493