| Full text | |
| Author(s): |
Vielma Leal, Francisco J.
;
Pastor, Ademir
Total Authors: 2
|
| Document type: | Journal article |
| Source: | ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS; v. 28, p. 42-pg., 2022-08-02. |
| Abstract | |
This paper is concerned with controllability and stabilization properties of the dispersion generalized Benjamin equation on the periodic domain T: First, by assuming the control input acts on all the domain, the system is proved to be globally exactly controllable in the Sobolev space H-p(s)(T), with s >= 0. Second, by providing a locally-damped term added to the equation as a feedback law, it is shown that the resulting equation is globally well-posed and locally exponentially stabilizable in the space L-p(2)(T). The main ingredient to prove the global well-posedness is the introduction of the dissipation-normalized Bourgain spaces which allows one to gain smoothing properties simultaneously from the dissipation and dispersion present in the equation. Finally, the local exponential stabilizability result is accomplished taking into account the decay of the associated semigroup combined with the fixed point argument. (AU) | |
| FAPESP's process: | 20/14226-4 - Dispersive equations: Controllability and stabilization in periodic domains |
| Grantee: | Francisco Javier Vielma Leal |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 19/02512-5 - Systems and partial differential equations |
| Grantee: | Marcelo da Silva Montenegro |
| Support Opportunities: | Research Projects - Thematic Grants |