Continuity of attractors for semilinear parabolic equations

• Grant number: 14/03685-7
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): August 01, 2014
• Effective date (End): December 13, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Alexandre Nolasco de Carvalho
• Grantee: Juliana Fernandes da Silva Pimentel
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

A better understanding of longtime dynamical properties of infinite dimensional dynamical systems generated by semilinear parabolic PDE's is of paramount relevance. The objective of this proposal is to indicate direction of research tobe pursued which in turn investigate the unbounded attractors associated to such systems under distinct perturbations (singular or not). The aim is to study unbounded attractors under perturbations that make the associated dynamical system dissipative. We also consider the phenomenon of homogenization and rate of convergence of unbounded attractors.

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)

BRUSCHI, SIMONE M.; CARVALHO, ALEXANDRE N.; PIMENTEL, JULIANA F. Limiting Grow-Up Behavior for a One-Parameter Family of Dissipative PDEs. Indiana University Mathematics Journal, v. 69, n. 2, p. 657-683, 2020. Web of Science Citations: 0.

PIMENTEL, JULIANA F. S. UNBOUNDED STURM GLOBAL ATTRACTORS FOR SEMILINEAR PARABOLIC EQUATIONS ON THE CIRCLE. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v. 48, n. 6, p. 3860-3882, 2016. Web of Science Citations: 1.