Differential and Integral Equations

Time optimal problems with boundary controls

J. P. Raymond and H. Zidani

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We consider time optimal control problems governed by semilinear parabolic equations with pointwise state constraints and unbounded controls. We derive a Pontryagin's principle for boundary controls. We prove a regularity result for the gradient of the state variable and by this way we are able to define a Hamiltonian functional which intervenes in an optimality condition satisfied by the optimal terminal time.

Article information

Differential Integral Equations, Volume 13, Number 7-9 (2000), 1039-1072.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49K20: Problems involving partial differential equations
Secondary: 35B37 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations


Raymond, J. P.; Zidani, H. Time optimal problems with boundary controls. Differential Integral Equations 13 (2000), no. 7-9, 1039--1072. https://projecteuclid.org/euclid.die/1356061209

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