1 |
S. A. Messaoudi, Blow up and global existence in a nonlinear viscoelastic wave equation, Math. Nachr., 260(2003), 58-66.
DOI
|
2 |
L. T. P. Ngoc, N. A. Triet and N. T. Long, On a nonlinear wave equation involving the term (x, t, u, ||ux||2)ux): Linear approximation and asymptotic expansion of solution in many small parameters, Nonlinear Anal. Real World Appl., 11(4)(2010), 2479-2510.
DOI
|
3 |
L. T. P. Ngoc, N. A. Triet, A. P. N. Dinh and N. T. Long, Existence and exponential decay of solutions for a wave equation with integral nonlocal boundary conditions of memory type, Numer. Funct. Anal. Optim., 38(9)(2017), 1173-1207.
DOI
|
4 |
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), 959-976.
DOI
|
5 |
Y. Ebihara, L. A. Medeiros and M. M. Miranda, Local solutions for a nonlinear degenerate hyperbolic equation, Nonlinear Anal., 10(1986), 27-40.
DOI
|
6 |
G. R. Kirchhoff, Vorlesungen uber Mathematische Physik: Mechanik, Teuber, Leipzig, 1876, Section 29.7.
|
7 |
N. A. Larkin, Global regular solutions for the nonhomogeneous Carrier equation, Math. Probl. Eng., 8(2002), 15-31.
DOI
|
8 |
I. Lasiecka, and J. Ong, Global solvability and uniform decays of solutions to quasilinear equation with nonlinear boundary dissipation, CComm. Partial Differential Equations, 24(11-12)(1999), 2069-2108.
DOI
|
9 |
J. L. Lions, Quelques methodes de resolution des problems aux limites non-lineares, Dunod; Gauthier-Villars, Paris, 1969.
|
10 |
N. T. Long, A. P. N. Dinh and T. N. Diem, Linear recursive schemes and asymptotic expansion associated with the Kirchhoff-Carrier operator, J. Math. Anal. Appl., 267(1)(2002), 116-134.
DOI
|
11 |
N. T. Long and L. T. P. Ngoc, On a nonlinear wave equation with boundary conditions of two-point type, J. Math. Anal. Appl., 385(2)(2012), 1070-1093.
DOI
|
12 |
L. A. Medeiros, On some nonlinear perturbation of Kirchhoff-Carrier operator, Mat. Apl. Comput., 13(1994), 225-233.
|
13 |
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), 871-884.
DOI
|
14 |
M. Milla Miranda and L. P. San Gil Jutuca, Existence and boundary stabilization of solutions for the Kirchhoff equation, Comm. Partial Differential Equations, 24(9-10)(1999), 1759-1800.
DOI
|
15 |
M. M. Cavalcanti, V. N. Domingos Cavalcanti and J. A. Soriano, Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation, Adv. Differential Equations, 6(6)(2001), 701-730.
|
16 |
M. M. Cavalcanti, V. N. Domingos Cavalcanti and J. A. Soriano, Global existence and asymptotic stability for the nonlinear and generalized damped extensible plate equation, Commun. Contemp. Math., 6(5)(2004), 705-731.
DOI
|
17 |
G. F. Carrier, On the nonlinear vibrations problem of elastic string, Quart. J. Appl. Math., 3(1945), 157-165.
DOI
|
18 |
M. Hosoya and Y. Yamada, On some nonlinear wave equation I: Local existence and regularity of solutions, J. Fac. Sci. Univ. Tokyo. Sect. IA, Math., 38(1991), 225-238.
|
19 |
L. X. Truong, L. T. P. Ngoc, A. P. N. Dinh and N. T. Long, Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type, Nonlinear Anal., 74(18)(2011), 6933-6949.
DOI
|
20 |
L. T. P. Ngoc, L. H. K. Son, T. M. Thuyet and N. T. Long, Linear approximation and asymptotic expansion of solutions for a nonlinear Carrier wave equation in an annular membrane with Robin-Dirichlet conditions, Math. Probl. Eng., 2016(2016), Article ID 8031638, 18 pages.
|
21 |
T. N. Rabello, M. C. C. Vieira, C. L. Frota and L. A. Medeiros, Small vertical vibrations of strings with moving ends, Rev. Mat. Complut., 16(2003), 179-206.
|
22 |
L. T. P. Ngoc and N. T. Long, Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions, Appl. Math., 61(2)(2016), 165-196.
DOI
|
23 |
L. H. K. Son, L. T. P. Ngoc and N. T. Long, Existence, blow-up and exponential decay estimates for the nonlinear Kirchhoff-Carrier wave equation in an annular with nonhomogeneous Dirichlet conditions, Filomat, 33(17)(2019), 5561-5588.
DOI
|
24 |
R. E. Showater, Hilbert space methods for partial differential equations, Electronic J. Differential Equations, Monograph 01, 1994.
|