| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 48 | |
| Number of page(s) | 48 | |
| DOI | https://doi.org/10.1051/cocv/2021036 | |
| Published online | 04 June 2021 | |
The turnpike property in semilinear control*
1
Departamento de Matemáticas, Universidad Autónoma de Madrid,
28049
Madrid, Spain.
2
Chair of Computational Mathematics, Fundación Deusto, University of Deusto,
48007,
Bilbao,
Basque Country, Spain.
** Corresponding author: dario.pighin@uam.es
Received:
13
April
2020
Accepted:
30
March
2021
An exponential turnpike property for a semilinear control problem is proved. The state-target is assumed to be small, whereas the initial datum can be arbitrary. Turnpike results are also obtained for large targets, requiring that the control acts everywhere. In this case, we prove the convergence of the infimum of the averaged time-evolution functional towards the steady one. Numerical simulations are performed.
Mathematics Subject Classification: 49N99 / 35K91
Key words: Optimal control problems / long time behavior / the turnpike property / semilinear parabolic equations
© EDP Sciences, SMAI 2021
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