Controllability under positivity constraints of semilinear heat equations
Entidad
UAM. Departamento de MatemáticasEditor
American Institute of Mathematical SciencesFecha de edición
2018-09-01Cita
10.3934/mcrf.2018041
Mathematical Control and Related Fields 8.3-4 (2018): 935-964
ISSN
2156-8472 (print); 2156-8499 (online)DOI
10.3934/mcrf.2018041Financiado por
This work was partially supported by the Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, FA9550-15-1-0027 of AFOSR, FA9550-14-1-0214 of the EOARD-AFOSR, the MTM2014-52347 and MTM2017 Grants of the MINECO (Spain) and ICON of the French ANRProyecto
Gobierno de España. MTM2014-52347; Gobierno de España. MTM2017-92996; info:eu-repo/grantAgreement/EC/H2020/694126/EU//DYCONVersión del editor
https://doi.org/10.3934/mcrf.2018041Materias
Controllability under constraints; Dissipativity; Iterative method; Semilinear heat equations; Waiting time; MatemáticasNota
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematical Control and Related Fields following peer review. The definitive publisher-authenticated version Mathematical Control and Related Fields 8.3-4 (2018): 935-964 is available online at: http://www.aimsciences.org/article/doi/10.3934/mcrf.2018041Derechos
© 2018, American Institute of Mathematical Sciences. All rights reservedResumen
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the control, when the time horizon is long enough. As we shall see, in fact, the minimal controllability time turns out to be strictly positive. More precisely, we prove a global steady state constrained controllability result for a semilinear parabolic equation with C 1 nonlinearity, without sign or globally Lipschitz assumptions on the nonlinear term. Then, under suitable dissipativity assumptions on the system, we extend the result to any initial datum and any target trajectory. We conclude with some numerical simulations that confirm the theoretical results that provide further information of the sparse structure of constrained controls in minimal time
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Google Scholar:Pighin, Dario
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Zuazua Iriondo, Enrique
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