Advances in Differential Equations

Stability for a system of wave equations of Kirchhoff with coupled nonlinear and boundary conditions of memory type

J. Ferreira and M. L. Santos

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Abstract

In this paper, we consider a system of two wave equations of Kirchhoff with coupled nonlinear and memory conditions at the boundary, and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decays with the same rate of decay of the relaxation functions; that is, the energy decays exponentially when the relaxation functions decay exponentially and polynomially when the relaxation functions decay polynomially.

Article information

Source
Adv. Differential Equations Volume 8, Number 7 (2003), 873-896.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355926815

Mathematical Reviews number (MathSciNet)
MR1988682

Zentralblatt MATH identifier
1030.35113

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34K20: Stability theory 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35B35: Stability 74H45: Vibrations

Citation

Santos, M. L.; Ferreira, J. Stability for a system of wave equations of Kirchhoff with coupled nonlinear and boundary conditions of memory type. Adv. Differential Equations 8 (2003), no. 7, 873--896. https://projecteuclid.org/euclid.ade/1355926815.


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