We study one class of fluid dynamic models in vector-valued optimization statement. The model consists of a system of two hyperbolic conservation laws with a source term: a nonlinear conservation law for the goods density and an evolution equation for the processing rate. We consider the case when the objective space is the Banach space Llpoc (RN ) partially ordered by the natural ordering cone of positive elements. We derive sufficient conditions for the existence of efficient controls. In the case, when the original control problem is not regular and may fail to have the entropy solutions, we discuss the regularization approach and prove the existence of the so-called efficient regularizators to the original vector-valued optimization problem.
Efficient Controls for One Class of Fluid Dynamic Models
D'APICE, Ciro;MANZO, Rosanna
2010
Abstract
We study one class of fluid dynamic models in vector-valued optimization statement. The model consists of a system of two hyperbolic conservation laws with a source term: a nonlinear conservation law for the goods density and an evolution equation for the processing rate. We consider the case when the objective space is the Banach space Llpoc (RN ) partially ordered by the natural ordering cone of positive elements. We derive sufficient conditions for the existence of efficient controls. In the case, when the original control problem is not regular and may fail to have the entropy solutions, we discuss the regularization approach and prove the existence of the so-called efficient regularizators to the original vector-valued optimization problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
