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Dynamics of autonomous and nonautonomous semilinear problems

Grant number: 14/03109-6
Support type:Regular Research Grants
Duration: June 01, 2014 - May 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Marcelo José Dias Nascimento
Grantee:Marcelo José Dias Nascimento
Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Assoc. 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. Web of Science Citations: 2.
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. Web of Science Citations: 4.
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. Web of Science Citations: 2.

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