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- Title
Existence of an Optimal Control for a Semilinear Evolution Equation with Unbounded Operator.
- Authors
Chernov, A. V.
- Abstract
An optimal control problem is investigated for an abstract semilinear differential equation of the first order in time in a Hilbert space with an unbounded operator and control involved linearly in the right-hand side. The cost functional is assumed to be additively separated with respect to state and control, with a rather general dependence on the state. For this problem, the existence of an optimal control is proved and the properties of the set of optimal controls are established. The author's previous results on the total preservation of unique global solvability (totally global solvability) and on solution estimation for such equations are developed in the context of the nonlinearity of the equation under study. The indicated estimate is found important for the present study. A nonlinear heat equation and a nonlinear wave equation are considered as examples.
- Subjects
OPERATOR equations; DIFFERENTIAL equations; NONLINEAR equations; EVOLUTION equations; HILBERT space; HEAT equation; NONLINEAR wave equations; WAVE equation
- Publication
Computational Mathematics & Mathematical Physics, 2024, Vol 64, Issue 5, p967
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S0965542524700362