Non-autonomous systems with impulses: convergent systems and the Navier-Stokes Equation

• Grant number: 12/16709-6
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2012
• End date: October 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Everaldo de Mello Bonotto
• Grantee: Everaldo de Mello Bonotto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The present project of scientific research concerns about the theory of systems which describe the evolution of process whose continuous dynamics are interrupted by abrupt changes of state. This phenomenon is called impulse. In many natural phenomena, the real deterministic models are often described by systems which involve impulses. By using the impulsive differential equation theory, this project lies on the investigation of convergent non-autonomous systems and the investigation of the non-autonomous Navier-Stokes equation with impulses. First, we intend to study properties of convergent systems. In the sequel, we shall study the attractor theory and the existence of almost periodic and recorrent solutions for the non-autonomous Navier-Stokes equation with impulses. The mathematical analysis of such systems employs techniques of classical functional analysis and dynamical system theory. (AU)

Scientific publications

(7)

(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)

BONOTTO, E. M.; MESQUITA, J. G.; SILVA, R. P.. Global Mild Solutions for a Nonautonomous 2D Navier-Stokes Equations with Impulses at Variable Times. Journal of Mathematical Fluid Mechanics, v. 20, n. 2, p. 801-818, JUN 2018. (12/16709-6, 14/16165-1, 16/24711-1, 12/08473-2)

BONOTTO, E. M.; JIMENEZ, M. Z.. Weak almost periodic motions, minimality and stability in impulsive semidynamical systems. Journal of Differential Equations, v. 256, n. 4, p. 1683-1701, FEB 15 2014. (10/12250-3, 12/16709-6)

BONOTTO, E. M.; DEMUNER, D. P.; JIMENEZ, M. Z.. Convergence for non-autonomous semidynamical systems with impulses. Journal of Differential Equations, v. 266, n. 1, p. 227-256, JAN 5 2019. (12/16709-6)

BONOTTO, E. M.; BORTOLAN, M. C.; CARVALHO, A. N.; CZAJA, R.. Global attractors for impulsive dynamical systems - a precompact approach. Journal of Differential Equations, v. 259, n. 7, p. 2602-2625, OCT 5 2015. (12/16709-6, 12/23724-1)

BONOTTO, EVERALDO DE MELLO; FERREIRA, JAQUELINE DA COSTA. Dissipativity in impulsive systems via Lyapunov functions. Mathematische Nachrichten, v. 289, n. 2-3, p. 213-231, FEB 2016. (12/16709-6)

AFONSO, S. M.; BONOTTO, E. M.; JIMENEZ, M. Z.. Negative trajectories in impulsive semidynamical systems. Journal of Differential Equations, v. 259, n. 3, p. 964-988, AUG 5 2015. (10/12250-3, 12/16709-6)

BONOTTO, E. M.; GIMENES, L. P.; SOUTO, G. M.. On Jack Hale's problem for impulsive systems. Journal of Differential Equations, v. 259, n. 2, p. 642-665, JUL 15 2015. (12/20933-9, 12/16709-6)