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Asymptotic stability of nonlinear hyperbolic equations

Grant number: 10/12202-9
Support Opportunities:Regular Research Grants
Duration: November 01, 2010 - October 31, 2012
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Ma To Fu
Grantee:Ma To Fu
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main subject of this project is the study of the long-time behavior of solutions of certain hyperbolic evolution equations by means of the theory of infinite dimensional dynamical systems. In view of the applicability of such differential equations in engineering and technology, this project integrates mathematical modeling and mathematical analysis of several real world problems. It also contributes to the development of new methods for the control and stabilization of dissipative systems. Specially for problems of vibrations of plates, thermo and visco-elastic systems, and modeling of special materials. To these problems, one discuses the global solvability, asymptotic stability and existence of attractors. The present project also integrates some doctoral dissertation projects. (AU)

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Scientific publications (7)
(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)
MA, TO FU; MUNOZ RIVERA, JAIME EDILBERTO; OQUENDO, HIGIDIO PORTILLO; SOBRADO SUAREZ, FREDY MAGLORIO. Polynomial stabilization of magnetoelastic plates. IMA JOURNAL OF APPLIED MATHEMATICS, v. 79, n. 2, p. 241-253, . (10/12202-9)
MA, T. F.; NARCISO, V.; PELICER, M. L.. Long-time behavior of a model of extensible beams with nonlinear boundary dissipations. Journal of Mathematical Analysis and Applications, v. 396, n. 2, p. 694-703, . (10/12202-9)
JORGE SILVA, M. A.; MA, T. F.. On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type. IMA JOURNAL OF APPLIED MATHEMATICS, v. 78, n. 6, p. 1130-1146, . (08/00123-7, 10/12202-9)
MA, T. F.; PELICER, M. L.. ATTRACTORS FOR WEAKLY DAMPED BEAM EQUATIONS WITH p-LAPLACIAN. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, n. S, SI, p. 525-534, . (10/12202-9)
JORGE SILVA, MARCIO ANTONIO; MA, TO FU. Long-time dynamics for a class of Kirchhoff models with memory. Journal of Mathematical Physics, v. 54, n. 2, . (08/00123-7, 10/12202-9)
ARAUJO, RAWLILSON DE OLIVEIRA; MA, TO FU; QIN, YUMING. Long-time behavior of a quasilinear viscoelastic equation with past history. Journal of Differential Equations, v. 254, n. 10, p. 4066-4087, . (10/12202-9)
ANDRADE, D.; JORGE SILVA, M. A.; MA, T. F.. Exponential stability for a plate equation with p-Laplacian and memory terms. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 35, n. 4, p. 417-426, . (08/00123-7, 10/12202-9)

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