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First and Second Order Optimality Conditions for the Control of Fokker-Planck Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Aronna, Maria Soledad Troltzsch, Fredi |
| Copyright Year | 2020 |
| Abstract | In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly multidimensional, and the function $B$ depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic (Tikhonov regularizing) term on the control. For this problem we prove existence of optimal control, first order necessary conditions, and second order necessary and sufficient conditions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/2002.03988v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
