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Dynamic systems in infinite dimensional spaces

Abstract

In this project, we are interested in studying dynamic systems generated by partial differential equations in spaces of infinite dimension, which can be parabolic or hyperbolic equations, when the parameters involved in the equations are submitted to perturbations. The main parameters of interest are the domain of definition of the solutions and the nonlinear terms in the equations, which may be concentrated in a neighborhood of the boundary of domain. Dynamic systems in infinite dimensional spaces are mathematical models for a large number of problems in applied areas such as physics, biology, chemistry, economics and engineering, among many others. Moreover, the equilibrium points of these models are solutions of elliptic partial differential equations. We analyze the existence and uniqueness of solutions, the asymptotic behavior of these solutions, the existence of global attractors, the continuity of equilibria and attractors in relation to the perturbation of the parameters. (AU)

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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)
ARAGAO, GLEICIANE S.; BEZERRA, FLANK D. M.; FIGUEROA-LOPEZ, RODIAK N.; NASCIMENTO, MARCELO J. D. Continuity of pullback attractors for evolution processes associated with semilinear damped wave equations with time-dependent coefficients. Journal of Differential Equations, v. 298, p. 30-67, OCT 15 2021. Web of Science Citations: 0.
BEZERRA, FLANK D. M.; ARAGAO, GLEICIANE S. LOWER SEMICONTINUITY OF THE PULLBACK ATTRACTORS OF NON-AUTONOMOUS DAMPED WAVE EQUATIONS WITH TERMS CONCENTRATING ON THE BOUNDARY. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 57, n. 1, p. 173-199, MAR 2021. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.