Continuity of attractors to parabolic problems

• Grant number: 11/04166-5
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2011
• End date: July 31, 2013
• 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
• City of the host institution: São Carlos
• Associated researchers: Flank David Morais Bezerra ; Jacson Simsen ; Karina Schiabel ; Mariza Stefanello Simsen ; Ricardo Parreira da Silva ; Vera Lucia Carbone

Abstract

The aim of this project is to study the asymptotic behavior of autonomous and non-autonomous parabolic problems. Weintend to consider semilinear (or nonlinear) partial differential equations involving an unbounded operator which is the infinitesimalgenerator of a $C_0$-semigroup (analytic or not). In the non-autonomous 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 also consider non-autonomous partial differential equations involving p-Laplacian operator. We will consider the nonlinearities with critical and subcritical growths. (AU)

Scientific publications

(8)

(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)

DA SILVA, SEVERINO HORACIO; BEZERRA, FLANK D. M.. FINITE FRACTAL DIMENSIONALITY OF ATTRACTORS FOR NONLOCAL EVOLUTION EQUATIONS. Electronic Journal of Differential Equations, SEP 4 2013. (11/04166-5)

ARARUNA, FAGNER DIAS; MORAIS BEZERRA, FLANK DAVID. RATE OF ATTRACTION FOR A SEMILINEAR WAVE EQUATION WITH VARIABLE COEFFICIENTS AND CRITICAL NONLINEARITIES. PACIFIC JOURNAL OF MATHEMATICS, v. 266, n. 2, p. 257-282, DEC 2013. (11/04166-5)

BEZERRA, FLANK D. M.; PEREIRA, ANTONIO L.; DA SILVA, SEVERINO H.. Existence and continuity of global attractors and nonhomogeneous equilibria for a class of evolution equations with non local terms. Journal of Mathematical Analysis and Applications, v. 396, n. 2, p. 590-600, DEC 15 2012. (11/04166-5, 03/10042-0)

BEZERRA, FLANK DAVID M.; NASCIMENTO, MARCELO JOSE D.. Convergence estimates of the dynamics of a hyperbolic system with variable coefficients. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 37, n. 5, p. 663-675, MAR 30 2014. (11/04166-5)

SIMSEN, JACSON; NASCIMENTO, MARCELO J. D.; SIMSEN, MARIZA S.. Existence and upper semicontinuity of pullback attractors for non-autonomous p-Laplacian parabolic problems. Journal of Mathematical Analysis and Applications, v. 413, n. 2, p. 685-699, MAY 15 2014. (11/04166-5)

CARVALHO, ALEXANDRE N.; CHOLEWA, JAN W.; NASCIMENTO, MARCELO J. D.. ON THE CONTINUATION OF SOLUTIONS OF NON-AUTONOMOUS SEMILINEAR PARABOLIC PROBLEMS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 59, n. 1, p. 17-55, FEB 2016. (11/51704-2, 11/04166-5)

BEZERRA, F. D. M.; NASCIMENTO, M. J. D.; DA SILVA, S. H.. Asymptotic behavior of solutions to a class of nonlocal non-autonomous diffusion equations. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 38, n. 17, p. 4317-4329, NOV 30 2015. (11/04166-5)

DA SILVA, SEVERINO HORACIO; BEZERRA, FLANK D. M.. FINITE FRACTAL DIMENSIONALITY OF ATTRACTORS FOR NONLOCAL EVOLUTION EQUATIONS. Electronic Journal of Differential Equations, v. N/A, p. 9-pg., 2013-09-04. (11/04166-5)