Existence of solutions for a Boussinesq system on the half line and on a finite interval

Discrete and Continuous Dynamical Systems

Volumn 29, Issue 1, 2011, Pages 25-49

  Adamy, Karine ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79954607430     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2011.29.25     Document Type: Article

References (15)

1. C. J. Amick, Regularity and uniqueness of solutions to the boussinesq system of equations, J. Diff. Eq., 54 (1984), 231-247.
2. T. B. Benjamin, "Lectures on Nonlinear Wave Motion," Lectures in Applied Mathematics, Vol. 15, Amer. Math. Soc., Providence, R.I., 1974.
3. J. Bona and R. Smith, A model for the two-way propagation of water waves in a channel, Math. Proc.Cambridge Philos., Soc., 79 (1976), 167-182.
4. J. Bona and V. Dougalis, An initial and boundary-value problem for a model equation for propagation of long waves, J. Math. Anal Appl., 75 (1980), 503-522.
5. J. 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. (Pubitemid 135699336)
6. J. 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. (Pubitemid 38671180)
7. J. R. Cannon, "The One-dimensional Heat Equation," Encyclopedia of Mathematics and its Applications, 23, 1984.
8. N. Dunford and J. Schwartz, "Linear Operators. Part I," Pure and Applied Mathematics, Vol. VII, Interscience Publishers, New York, 1988.
9. A. S. Fokas and B. Pelloni, Boundary value problems for Boussinesq type systems, Math. Phys., Anal. Geom., 8 (2005), 59-96. (Pubitemid 40550372)
10. A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice Hall, Englewood Cliffs, N.J. 1964.
11. P. D. Lax, "Shock Waves and Entropy," in Contributions to Non-Linear Functionnal Analysis, Academic Press, 1971.
12. M. M. Rao and Z. D. Ren, "Theory of Orlicz Spaces," Monographs and Textbooks in Pure and Applied Mathematics, 146, Marcel Dekker Inc., New York, 1991.
13. W. Rudin, "Functionnal Analysis," McGraw-Hill, New York, 1973.
14. M. E. Schonbek, Existence of solutions for the Boussinesq system of equations, J. Differential Equations, 42 (1981), 325-352.
15. G. B. Whitham, "Linear and Nonlinear Waves," Pure and Applied Mathematics, Wiley- Interscience, New-York-London-Sydney, 1974.