Free Access
Issue
ESAIM: M2AN
Volume 41, Number 5, September-October 2007
Page(s) 825 - 854
DOI https://doi.org/10.1051/m2an:2007043
Published online 23 October 2007
  1. A.A. Alazman, J.P. Albert, J.L. Bona, M. Chen and J. Wu, Comparisons between the BBM equation and a Boussinesq system. Adv. Differential Equations 11 (2006) 121–166. [MathSciNet] [Google Scholar]
  2. D.C. Antonopoulos, The Boussinesq system of equations: Theory and numerical analysis. Ph.D. Thesis, University of Athens, 2000 (in Greek). [Google Scholar]
  3. D.C. Antonopoulos, V.A. Dougalis and D.E. Mitsotakis, Theory and numerical analysis of the Bona-Smith type systems of Boussinesq equations. (to appear). [Google Scholar]
  4. J.L. Bona and M. Chen, A Boussinesq system for two-way propagation of nonlinear dispersive waves. Physica D 116 (1998) 191–224. [CrossRef] [MathSciNet] [Google Scholar]
  5. J.L. Bona and R. Smith, A model for the two-way propagation of water waves in a channel. Math. Proc. Camb. Phil. Soc. 79 (1976) 167–182. [CrossRef] [Google Scholar]
  6. J.L. Bona, M. Chen and J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: I. Derivation and Linear Theory. J. Nonlinear Sci. 12 (2002) 283–318. [CrossRef] [MathSciNet] [Google Scholar]
  7. 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) 925–952. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.L. Bona, T. Colin and D. Lannes, Long wave approximations for water waves. Arch. Rational Mech. Anal. 178 (2005) 373–410. [CrossRef] [MathSciNet] [Google Scholar]
  9. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York (1994). [Google Scholar]
  10. M. Chen, Exact traveling-wave solutions to bi-directional wave equations. Int. J. Theor. Phys. 37 (1998) 1547–1567. [CrossRef] [Google Scholar]
  11. M. Chen, Solitary-wave and multi pulsed traveling-wave solutions of Boussinesq systems. Applic. Analysis 75 (2000) 213–240. [CrossRef] [Google Scholar]
  12. V.A. Dougalis and D.E. Mitsotakis, Solitary waves of the Bona-Smith system, in Advances in scattering theory and biomedical engineering, D. Fotiadis and C. Massalas Eds., World Scientific, New Jersey (2004) 286–294. [Google Scholar]
  13. V.A. Dougalis, D.E. Mitsotakis and J.-C. Saut, On initial-boundary value problems for some Boussinesq systems in two space dimensions. (to appear). [Google Scholar]
  14. P. Grisvard, Quelques proprietés des espaces de Sobolev, utiles dans l'étude des équations de Navier-Stokes (I). Problèmes d'évolution, non linéaires, Séminaire de Nice (1974–1976). [Google Scholar]
  15. D.R. Kincaid, J.R. Respess, D.M. Young and R.G. Grimes, ITPACK 2C: A Fortran package for solving large sparse linear systems by adaptive accelerated iterative methods. ACM Trans. Math. Software 8 (1982) 302–322. [CrossRef] [Google Scholar]
  16. R. Rannacher and R. Scott, Some optimal error estimates for piecewise linear finite element approximations. Math. Comp. 38 (1982) 437–445. [CrossRef] [MathSciNet] [Google Scholar]
  17. A.H. Schatz and L.B. Wahlbin, On the quasi-optimality in L of the Formula -projection into finite elements spaces. Math. Comp. 38 (1982) 1–22. [MathSciNet] [Google Scholar]
  18. M.H. Schultz, L Multivariate approximation theory. SIAM J. Numer. Anal. 6 (1969) 161–183. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.H. Schultz, Approximation theory of multivatiate spline functions in Sobolev spaces. SIAM J. Numer. Anal. 6 (1969) 570–582. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.F. Toland, Existence of symmetric homoclinic orbits for systems of Euler-Lagrange equations. A.M.S. Proc. Symposia in Pure Mathematics 45 (1986) 447–459. [Google Scholar]
  21. G.B. Whitham, Linear and Non-linear Waves. Wiley, New York (1974). [Google Scholar]

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