Dynamics of autonomous and nonautonomous semilinear problems

• Grant number: 14/03109-6
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2014
• End date: May 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo José Dias Nascimento
• Grantee: Marcelo José Dias Nascimento
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Flank David Morais Bezerra ; Karina Schiabel ; Vera Lucia Carbone

Abstract

The aim of this project is to study evolution problems arising from semilinear equations, partial differential equations typically parabolic and hyperbolic semilinear autonomous or nonautonomous. We intend to consider semilinear partial differential equations (or nonlinear), involving an unbounded operator which is the infinitesimal generator of a C_0-semigroup (analytic or not). In the nonautonomous case, the operator will depend on the time t, instead of the explicit time dependence be just in the nonlinearity, as generally found in the literature. We will study parabolic approximations of hyperbolic problems (using fractional powers) and we try to transfer information of the parabolic problem (more generous with the class of nonlinearities) for the hyperbolic problem. In addition, we search for results of existence of pullback attractor for a parabolic plate equation as the nonlinearity has a critical growth. Additionally, we will study the existence of pullback exponential attractors for nonautonomous semilinear problems. (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)

BEZERRA, FLANK D. M.; CARBONE, VERA L.; NASCIMENTO, MARCELO J. D.; SCHIABEL, KARINA. PULLBACK ATTRACTORS FOR A CLASS OF NON-AUTONOMOUS THERMOELASTIC PLATE SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 23, n. 9, p. 3553-3571, NOV 2018. (14/03686-3, 14/03109-6)

BEZERRA, F. D. M.; NASCIMENTO, M. J. D.; DA SILVA, S. H.. A class of dissipative nonautonomous nonlocal second-order evolution equations. APPLICABLE ANALYSIS, v. 96, n. 13, p. 2180-2191, 2017. (14/03686-3, 14/03109-6)

BEZERRA, F. D. M.; CARVALHO, A. N.; CHOLEWA, J. W.; NASCIMENTO, M. J. D.. Parabolic approximation of damped wave equations via fractional powers: Fast growing nonlinearities and continuity of the dynamics. Journal of Mathematical Analysis and Applications, v. 450, n. 1, p. 377-405, JUN 1 2017. (14/03686-3, 14/03109-6, 03/10042-0)