Advances in Differential Equations
- Adv. Differential Equations
- Volume 8, Number 7 (2003), 873-896.
Stability for a system of wave equations of Kirchhoff with coupled nonlinear and boundary conditions of memory type
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.
Adv. Differential Equations Volume 8, Number 7 (2003), 873-896.
First available in Project Euclid: 19 December 2012
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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