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THE INITIAL-BOUNDARY-VALUE PROBLEM OF A GENERALIZED BOUSSINESQ EQUATION ON THE HALF LINE
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 Title & Authors
THE INITIAL-BOUNDARY-VALUE PROBLEM OF A GENERALIZED BOUSSINESQ EQUATION ON THE HALF LINE
Xue, Ruying;
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 Abstract
The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing he Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation
 Keywords
Boussinesq equation;existence;initial-boundary-value problem;
 Language
English
 Cited by
 References
1.
J. L. Bona, M. Chen, and J. C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media II: The nonlinear theory, Nonlinearity 17 (2004), no. 3, 925-952 crossref(new window)

2.
J. L. Bona and R. L. Sachs, Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation, Comm. Math. Phys. 118 (1988), no. 1, 15-29 crossref(new window)

3.
J. L. Bona, S. M. Sun, and B. Y. Zheng, A non-homogenous boundary-value problem for the Korteweg-de-Varies equation in a quarter plane, Trans. Amer. Math. Soc. 326 (2001), 427-490

4.
J. E. Colliander and C. E. Kenig, The generalized Korteweg-de Vries equation on the half line, Comm. Partial Differential Equations 27 (2002), no. 11-12, 2187-2266 crossref(new window)

5.
J. Holmer, The initial-boundary value problem for the Korteweg-de Vries equation, Comm. Partial Differential Equations 31 (2006), no. 8, 1151-1190 crossref(new window)

6.
C. E. Kenig, G. Ponce, and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), no. 1, 33-69 crossref(new window)

7.
C. E. Kenig, G. Ponce, and G. Velo, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. 46 (1993), no. 4, 527-620 crossref(new window)

8.
F. Linares, Global existence of small solutions for a generalized Boussinesq equation, J. Differential Equations 106 (1993), no. 2, 257-293 crossref(new window)

9.
L. Molinet and F. Ribaud, On the Cauchy problem for the generalized Korteweg-de Vries equation, Comm. Partial Differential Equations 28 (2003), no. 11-12, 2065-2091 crossref(new window)

10.
A. K. Pani and H. Saranga, Finite element Galerkin method for the "good" Boussinesq equation, Nonlinear Anal. 29 (1997), no. 8, 937-956 crossref(new window)

11.
V. Varlamov, Long-time asymptotics for the damped Boussinesq equation in a disk, Electron. J. Diff. Eqns., Conf. 05 (2000), 285-298

12.
R. Xue, Local and global existence of solutions for the Cauchy problem of a generalized Boussinesq equation, J. Math. Anal. Appl. 316 (2006), no. 1, 307-327 crossref(new window)