References
- J. J. Bae, On uniform decay of coupled wave equation of Kirchhoff type subject to memory condition on the boundary, Nonlinear Anal. 61 (2005), no. 3, 351-372 https://doi.org/10.1016/j.na.2004.11.014
- G. F. Carrier, On the non-linear vibration problem of the elastic string, Quart. Appl. Math. 3 (1945), 157-165 https://doi.org/10.1090/qam/12351
- M. M. Cavalcanti, V. N. Domingos Cavalcanti, and M. L. Santos, Existence and uniform decay rates of solutions to a degenerate system with memory conditions at the boundary, Appl. Math. Comput. 150 (2004), no. 2, 439-465 https://doi.org/10.1016/S0096-3003(03)00284-4
- A. T. Cousin, C. L. Frota, N. A. Lar'kin, and L. A. Medeiros, On the abstract model of the Kirchhoff-Carrier equation, Commun. Appl. Anal. 1 (1997), no. 3, 389-404
- C. L. Frota , A. T. Cousin, and L. A. Lar'kin, Existence of global solutions and energy decay for the Carrier equation with dissipative term, Differential Integral Equations 12 (1999), no. 4, 453-469
- T. Matsuyama, Quasilinear hyperbolic-hyperbolic singular perturbations with nonmonotone nonlinearity, Nonlinear Anal. 35 (1999), no. 5, 589-607 https://doi.org/10.1016/S0362-546X(97)00737-2
-
N. T. Long, On the nonlinear wave equation
$u_{tt}\;-\;B(t,\;{\parallel}u{\parallel}^2,\;{\parallel}u_x{\parallel}^2)u_{xx}\;=\;f(x,\;t,\;u,\;u_x,\;u_t,\;{\parallel}u{\parallel}^2,\;{\parallel}u_x{\parallel}^2)$ associated with the mixed homogeneous conditions, J. Math. Anal. Appl. 306 (2005), no. 1, 243-268 https://doi.org/10.1016/j.jmaa.2004.12.053 - J. Y. Park, J. J. Bae, and I. H. Jung, On existence of global solutions for the carrier model with nonlinear damping and source terms, Appl. Anal. 77 (2001), no. 3-4, 305-318 https://doi.org/10.1080/00036810108840910
- J. Y. Park, J. J. Bae, and I. H. Jung, Uniform decay of solution for wave equation of Kirchhoff type with nonlinear boundary damping and memory term, Nonlinear Anal. 50 (2002), no. 7, 871-884 https://doi.org/10.1016/S0362-546X(01)00781-7
- M. L. Santos, J. Ferreira, D. C. Pereira, and C. A. Raposo, Global existence and stability for wave equation of Kirchhoff type with memory condition at the boundary, Nonlinear Anal. 54 (2003), no. 5, 959-976 https://doi.org/10.1016/S0362-546X(03)00121-4
Cited by
- General decay for a wave equation of Kirchhoff type with a boundary control of memory type vol.2011, pp.1, 2011, https://doi.org/10.1186/1687-2770-2011-55
- Control of a riser through the dynamic of the vessel vol.95, pp.9, 2016, https://doi.org/10.1080/00036811.2015.1080249
- Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type vol.23, pp.2, 2017, https://doi.org/10.1007/s10883-016-9310-2
- Uniform Stabilization of aNonlinear Axially Moving String by a Boundary Control of Memory Type 2018, https://doi.org/10.1007/s10883-017-9370-y