Controllability under positivity constraints of semilinear heat equations
Pighin D, Zuazua E (2018)
Publication Type: Journal article
Publication year: 2018
Journal
Book Volume: 8
Pages Range: 935-964
Journal Issue: 3-4
DOI: 10.3934/mcrf.2018041
Abstract
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 C1 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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Spain (ES)How to cite
APA:
Pighin, D., & Zuazua, E. (2018). Controllability under positivity constraints of semilinear heat equations. Mathematical Control and Related Fields, 8(3-4), 935-964. https://dx.doi.org/10.3934/mcrf.2018041
MLA:
Pighin, Dario, and Enrique Zuazua. "Controllability under positivity constraints of semilinear heat equations." Mathematical Control and Related Fields 8.3-4 (2018): 935-964.
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