Einstein constraints and differential equations on the sphere

• Grant number: 17/07882-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2017
• End date: October 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Phillipo Lappicy Lemos Gomes
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 18/18703-1 - Attractors for fully nonlinear parabolic equations and non-autonomous equations, BE.EP.PD

Abstract

During the period of pos-doctorate, I will study infinite dimensional dynamical systems. I pretend to continue developing the research I have pursued in my Phd thesis, which will be finished in the upcoming year at the Freie Universitaet Berlin. The proposed problems for such period are described below. Besides, I would like to meet several researches in the same research directions I am and to start new projects, aiming at contributing and pushing the brazilian mathematics forward.In order to continue my thesis I will be concerned about dynamical systems generated by parabolic differential equations, when the domain is spherical. Firstly, it arises the question how the symmetry of the domain influences the symmetry of the solutions of such equations. Secondly, it is of general interest to describe the asymptotic behaviour, that is, the global attractor, when the solutions are axial and hence the equation becomes spatially one dimensional. The application of such theory is the Einstein's Hamiltonian constraint equation and the construction of some initial conditions in the interior of black holes.In order to start new projects and meet new researches in Brazil interested in similar areas, I pretend to spend my period in São Carlos at ICMC-USP, under the orientation of Alexandre Carvalho.

Scientific publications

(5)

(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)

LAPPICY, PHILLIPO; FIEDLER, BERNOLD. A Lyapunov function for fully nonlinear parabolic equations in one spatial variable. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 13, n. 1, p. 283-291, JUN 2019. (17/07882-0)

LAPPICY, PHILLIPO; DANIEL, VICTOR HUGO. Chaos in spatially homogeneous Horava-Lifshitz subcritical cosmologies. Classical and Quantum Gravity, v. 39, n. 13, p. 18-pg., 2022-07-07. (18/18703-1, 20/07532-1, 17/07882-0)

LAPPICY, PHILLIPO. Sturm attractors for fully nonlinear parabolic equations. REVISTA MATEMATICA COMPLUTENSE, v. N/A, p. 23-pg., 2022-08-03. (18/18703-1, 17/07882-0)

DAI, JIA-YUAN; LAPPICY, PHILLIPO. Ginzburg-Landau Patterns in Circular and Spherical Geometries: Vortices, Spirals, and Attractors. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 20, n. 4, p. 1959-1984, 2021. (18/18703-1, 17/07882-0)

LAPPICY, PHILLIPO; PIMENTEL, JULIANA. Slowly non-dissipative equations with oscillating growth. PORTUGALIAE MATHEMATICA, v. 75, n. 3-4, p. 313-327, 2018. (16/04925-7, 17/07882-0)