Rigorous computations for PDEs

• Grant number: 13/07460-7
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2013
• End date: May 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant(s): 13/50382-7 - Rigorous computations for nonlinear partial differential equations, AP.R

Abstract

The goal of this research project is to rigorously compute (prove the existence of) solutions of PDEs. The goal is to extend the so-called rigorous continuation method to prove the existence ofsolutions of PDEs defined on non-rectangular domains or with non-periodic boundary conditions, and also to prove the existence of time-periodic solutions of PDEs. (AU)

Scientific publications

(11)

(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)

GAMEIRO, MARCIO; HIRAOKA, YASUAKI; OBAYASHI, IPPEI. Continuation of point clouds via persistence diagrams. PHYSICA D-NONLINEAR PHENOMENA, v. 334, p. 118-132, NOV 1 2016. (10/00875-9, 13/07460-7)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; PUGLIESE, ALESSANDRO. Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, v. 16, n. 2, p. 531-575, APR 2016. (10/00875-9, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; TEIXEIRA, MARCO A.; GAMEIRO, MARCIO. On Exponential Decay and the Markus-Yamabe Conjecture in Infinite Dimensions with Applications to the Cima System. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1199-1219, SEP 2018. (13/07460-7, 16/21032-6, 12/18780-0, 16/08704-5, 15/19165-5)

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)

RODRIGUES, HILDEBRANDO M.; WU, JIANHONG; GAMEIRO, MARCIO. SWITCHING SYNCHRONIZED CHAOTIC SYSTEMS APPLIED TO SECURE COMMUNICATION. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, v. 8, n. 2, p. 413-426, APR 2018. (13/07460-7, 16/08704-5, 16/21032-6, 10/00875-9, 14/12277-0)

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; HIRAOKA, YASUAKI; IZUMI, SHUNSUKE; KRAMAR, MIROSLAV; MISCHAIKOW, KONSTANTIN; NANDA, VIDIT. A topological measurement of protein compressibility. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, v. 32, n. 1, p. 1-17, MAR 2015. (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)

MIYAJI, TOMOYUKI; PILARCZYK, PAWEL; GAMEIRO, MARCIO; KOKUBU, HIROSHI; MISCHAIKOW, KONSTANTIN. A study of rigorous ODE integrators for multi-scale set-oriented computations. APPLIED NUMERICAL MATHEMATICS, v. 107, p. 34-47, SEP 2016. (10/00875-9, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; CARABALLO, TOMAS; GAMEIRO, MARCIO. DYNAMICS OF A CLASS OF ODES VIA WAVELETS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 16, n. 6, p. 2337-2355, NOV 2017. (13/07460-7, 16/21032-6, 16/08704-5, 15/19165-5)