Rigorous computations for nonlinear partial differential equations

• Grant number: 13/50382-7
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2013
• End date: October 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: Consortium of Alberta, Laval, Dalhousie and Ottawa (CALDO)
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Principal researcher abroad: Jean Phillippe Lessard
• Institution abroad: Université Laval, Canada
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07460-7 - Rigorous computations for PDEs, AP.R

Abstract

The goal of this research project is to understand global properties of PDEs by developing rigorous computational methods to prove existence of periodic orbits, connecting orbits and even chaotic dynamics for PDEs, with the long-term goal of unlocking the secrets hidden within the dynamics of complicated fluid mechanics models such as the Navier-Stokes equations and Rayleigh-Bénard convection. (AU)

Scientific publications

(4)

(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)

CASTELLI, ROBERTO; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation. Archive for Rational Mechanics and Analysis, v. 228, n. 1, p. 129-157, APR 2018. (16/08704-5, 16/21032-6, 13/50382-7, 13/07460-7)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 1, p. 687-728, 2017. (10/00875-9, 13/50382-7, 16/08704-5, 13/07460-7)

FIGUERAS, JORDI-LLUIS; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; DE LA LLAVE, RAFAEL. A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 2, p. 1070-1088, 2017. (16/08704-5, 13/50382-7, 10/00875-9, 13/07460-7)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; RICAUD, YANN. Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series. Journal of Computational and Applied Mathematics, v. 292, p. 654-673, JAN 15 2016. (13/50382-7, 10/00875-9, 13/07460-7)