대한수학회지 (Journal of the Korean Mathematical Society)

  • 제45권1호
  • /
  • Pages.79-95
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  • 2008
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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THE INITIAL-BOUNDARY-VALUE PROBLEM OF A GENERALIZED BOUSSINESQ EQUATION ON THE HALF LINE

  • Xue, Ruying (Department of Mathematics Zhejiang University)
  • 발행 : 2008.01.31
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초록

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

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참고문헌

  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 https://doi.org/10.1088/0951-7715/17/3/010
  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 https://doi.org/10.1007/BF01218475
  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 https://doi.org/10.1081/PDE-120016157
  5. J. Holmer, The initial-boundary value problem for the Korteweg-de Vries equation, Comm. Partial Differential Equations 31 (2006), no. 8, 1151-1190 https://doi.org/10.1080/03605300600718503
  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 https://doi.org/10.1512/iumj.1991.40.40003
  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 https://doi.org/10.1002/cpa.3160460405
  8. F. Linares, Global existence of small solutions for a generalized Boussinesq equation, J. Differential Equations 106 (1993), no. 2, 257-293 https://doi.org/10.1006/jdeq.1993.1108
  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 https://doi.org/10.1081/PDE-120025496
  10. A. K. Pani and H. Saranga, Finite element Galerkin method for the "good" Boussinesq equation, Nonlinear Anal. 29 (1997), no. 8, 937-956 https://doi.org/10.1016/S0362-546X(96)00093-4
  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 https://doi.org/10.1016/j.jmaa.2005.04.041