Controllability properties for dispersive models

• Grant number: 22/15647-9
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2023
• End date: March 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Miguel Dario Soto Vieira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this research project, we propose the study of well-posedness, local and global controllabilityof some mathematical models that describe the propagation of dispersive waves in thetheory of fluid and other fields of physical science. We will pay particular attention to the following models: the Boussinesq system, the kawahara equation, the Gear-Grimshaw system and a family of linear one-dimensional dispersive equations. For the Boussinesq system, it was recently proved the internal and boundary controllability in a periodic domain. We propose to obtain internal and boundary controllability considering a non-periodic but bounded domain, by using the Hilbert Uniqueness Method (HUM). For the Kawahara equation, it has already been established the internal controllability with constraints on the space of controllable data. We intend to obtain controllability, without these restrictions, by introducing in the equation an evanescent viscosity, and applying theMoment Method. For the Gear-Grimshaw system, it is known well-posedness and control results inthe case of bounded domains. We propose the study of these properties in the case of a periodicdomain, using the HUM method. In addition, for a family of one-dimensional linear dispersiveequations we propose the study of boundary controlability in a periodic domain.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MICU, SORIN; PAZOTO, ADEMIR F.; VIEIRA, MIGUEL D. SOTO. Boundary controllability of a higher-order Boussinesq system. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. N/A, p. 27-pg., 2024-08-28. (22/15647-9)