Uniform stability of a non-autonomous semilinear Bresse system with memory

被引：3

作者：

Araújo R.O. ^{[1
]}

Marinho S.S. ^{[2
]}

Prates Filho J.S. ^{[3
]}

机构：

[1] Department of Mathematics, Institute of Geosciences and Exact Sciences, São Paulo State University, Rio Claro, 13506-900, SP

[2] Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos, 13560-190, SP

[3] Department of Mathematics, State University of Maringá, Maringá, 87020-900, PR

来源：

Applied Mathematics and Computation | 2021年 / 387卷

关键词：

Bresse system; Energy decay; Infinite memory; Visco-elasticity;

D O I：

10.1016/j.amc.2019.04.074

中图分类号：

学科分类号：

摘要：

The Bresse system is a recognized mathematical model for vibrations of a circular arched beam that contains the class of Timoshenko beams when the arch's curvature is zero. It turns out that the majority of mathematical analysis to Bresse systems are concerned with the asymptotic stability of linear homogeneous problems. Under this scenario, we consider a nonlinear Bresse system modeling arched beams with memory effects, in a nonlinear elastic foundation. Then we establish uniform decay rates of the energy under time-dependent external forces. © 2019 Elsevier Inc.

引用

共 24 条

[1]

Alabau Boussouira F., Munoz Rivera J.E., Almeida Junior D.S., Stability to weak dissipative Bresse system, J. Math. Anal. Appl., 374, pp. 481-498, (2011)

[2]

Almeida Junior D.S., Santos M.L., Munoz Rivera J.E., Stability to weakly dissipative Timoshenko systems, Math. Methods Appl. Sci., 36, pp. 1965-1976, (2013)

[3]

Alves M.O., Fatori L.H., Jorge Silva M.A., Monteiro R.N., Stability and optimality of decay rate for a weakly dissipative Bresse system, Math. Methods Appl. Sci., 38, pp. 898-908, (2015)

[4]

Alves M.S., Jorge Silva M.A., Ma T.F., Munoz Rivera J.E., Non-homogeneous thermoelastic Timoshenko systems, Bull. Braz. Math. Soc., 48, pp. 461-484, (2017)

[5]

Bresse J.A.C., Cours de Méchanique Appliquée, (1859)

[6]

Chueshov I., Eller M., Lasiecka I., On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation, Comm. Part. Differ. Equ., 27, pp. 1901-1951, (2002)

[7]

Dafermos C.M., Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal., 37, pp. 297-308, (1970)

[8]

Dell'Oro F., Asymptotic stability of thermoelastic systems of Bresse type, J. Differ. Equ., 258, pp. 3902-3927, (2015)

[9]

Fatori L.H., Monteiro R.N., The optimal decay rate for a weak dissipative Bresse system, Appl. Math. Lett., 25, pp. 600-604, (2012)

[10]

Fatori L.H., Munoz Rivera J.E., Rates of decay to weak thermoelastic Bresse system, IMA J. Appl. Math., 75, pp. 881-904, (2010)

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