Optimal bilinear control for Gross-Pitaevskii equations with singular potentials
| dc.contributor.author | Wang, Kai | |
| dc.contributor.author | Zhao, Dun | |
| dc.date.accessioned | 2021-12-06T15:14:40Z | |
| dc.date.available | 2021-12-06T15:14:40Z | |
| dc.date.issued | 2019-10-13 | |
| dc.description.abstract | We study the optimal bilinear control problem of the generalized Gross-Pitaevskii equation i∂tu = -∆u + U(x)u + φ(t) 1/|x|α u + λ|u|2σu, x ∈ ℝ3, where U(x) is the given external potential, φ(t) is the control function. The existence of an optimal control and the optimality condition are presented for suitable α and σ. In particular, when 1 ≤ α < 3/2, the Fréchet-differentiability of the objective functional is proved for two cases: (i) λ < 0, 0 < σ < 2/3; (ii) λ > 0, 0 < σ < 2. Comparing with the previous studies in [6], the results fill the gap for σ ∈ (0, 1/2). | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Wang, K., & Zhao, D. (2019). Optimal bilinear control for Gross-Pitaevskii equations with singular potentials. Electronic Journal of Differential Equations, 2019(115), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15009 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Optimal bilinear control | |
| dc.subject | Gross-Pitaevskii equation | |
| dc.subject | Objective functional | |
| dc.subject | Frechet-differentiability | |
| dc.subject | Optimal condition | |
| dc.title | Optimal bilinear control for Gross-Pitaevskii equations with singular potentials | |
| dc.type | Article |