In this paper an optimal control problem for the elliptic boundary value problem with nonlocal boundary conditions is considered. It is shown that the weak solutions of the boundary value problem depend smoothly on the control parameter and that the cost functional of the optimal control problem is Frechet differentiable with respect to the control parameter.
Optimalus valdymas modeliuose su laidžiu-radioaktyviu šilumos pernešimu
Santrauka. Darbe nagrinėjamas nelokalaus kraštinio uždavinio optimalaus valdymo uždavinys. Parodyta, kad silpnasis kraštinio uždavinio sprendinys tolydžiai priklauso nuo valdomojo parametro, taigi, optimalaus valdymo tikslo funkcija yra diferencijuojama Freše prasme pagal valdomus parametrus.
Birgelis, K. (2003). Optimal control in models with conductive‐radiative heat transfer. Mathematical Modelling and Analysis, 8(1), 1-12. https://doi.org/10.3846/13926292.2003.9637205
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