We study one class of nonlinear fluid dynamic models with controls in the initial condition and the source term. The model is described by a nonlinear inhomogeneous hyperbolic conservation law with state and control constraints. We consider the case when the greatest lower bound of the cost functional can be unattainable on the set Ξ of admissible pairs or the set Ξ is possibly empty. Using the methods of vector-valued optimization theory, we show that this optimal control problem admits the existence of the so-called weakened approximate solution which can be interpreted as generalized solution to some vector optimization problem of special form.
On Vector-Valued Approximation of State Constrained Optimal Control Problems for Nonlinear Hyperbolic Conservation Laws
MANZO, Rosanna
2013-01-01
Abstract
We study one class of nonlinear fluid dynamic models with controls in the initial condition and the source term. The model is described by a nonlinear inhomogeneous hyperbolic conservation law with state and control constraints. We consider the case when the greatest lower bound of the cost functional can be unattainable on the set Ξ of admissible pairs or the set Ξ is possibly empty. Using the methods of vector-valued optimization theory, we show that this optimal control problem admits the existence of the so-called weakened approximate solution which can be interpreted as generalized solution to some vector optimization problem of special form.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
