Asymptotic analysis of autonomous and non-autonomous parabolic problems

• Grant number: 19/20341-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2020
• End date: March 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Tito Luciano Mamani Luna
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We will see that the proposal developed mainly addresses qualitative issues associated with the study of the existence and characterization of the global attractor structure for some classes of nonlinear (autonomous and nonautonomous) parabolic problems with the presence of a Kirchhoff term in the operator. To solve such problems, we propose to combine variational and topological techniques; and techniques from the study of nonlinear dynamical systems: sub-super solutions, a-priori estimates, among others. (AU)

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)

LUNA, T. L. M.; CARVALHO, A. N.. A bifurcation problem for a one-dimensional p-Laplace elliptic problem with non-odd absorption. Journal of Differential Equations, v. 373, p. 30-pg., 2023-11-15. (19/20341-3, 20/14075-6)

LI, YANAN; CARVALHO, ALEXANDRE N.; LUNA, TITO L. M.; MOREIRA, ESTEFANI M.. A NON-AUTONOMOUS BIFURCATION PROBLEM FOR A NON-LOCAL SCALAR ONE-DIMENSIONAL PARABOLIC EQUATION. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 19, n. 11, p. 5181-5196, NOV 2020. (19/20341-3, 18/10997-6, 18/00065-9)