| Autor: |
Jesus IP; Universidade Federal do Piauí, DM, Campus Universitário Ministro Petrônio Portella, Bairro Ininga, SG-4, Av. Universitária, s/n, 64049-550 Teresina, PI, Brazil., Clark MR; Universidade Federal do Piauí, DM, Campus Universitário Ministro Petrônio Portella, Bairro Ininga, SG-4, Av. Universitária, s/n, 64049-550 Teresina, PI, Brazil., Oliveira AM; Universidade Federal do Delta do Parnaíba, DM, bairro Nossa Senhora de Fátima, Av. São Sebastião, 2819, 64202-020 Parnaíba, PI, Brazil., Lourêdo AT; Universidade Federal do Delta do Parnaíba, DM, bairro Nossa Senhora de Fátima, Av. São Sebastião, 2819, 64202-020 Parnaíba, PI, Brazil.; Universidade Estadual da Paraíba, DM, Rua Baraúnas, Bairro Universitário, 351, 58429-500 Campina Grande, PB, Brazil. |
| Abstrakt: |
This manuscript deals with a hierarchical control problem for Oldroyd equation under the Stackelberg-Nash strategy. The Oldroyd equation model is defined by non-regular coefficients, that is, they are bounded measurable functions. We assume that we can act in the dynamic of the system by a hierarchy of controls, where one main control (the leader) and several additional secondary control (the followers) act in order to accomplish their given tasks: controllability for the leader and optimization for followers. We obtain the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability with respect to the leader control, and the optimality system for leader control. |
