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

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  • The initial boundary-value problem for a Boussinesq system is studied on the half line and on a finite interval. Global existence of weak solutions satisfying the boundary conditions is proven and uniqueness for solutions in a suitable class is studied. A proof of the persistence of finite regularity for solutions in the whole space is also presented.
    Mathematics Subject Classification: 35A01, 35F61, 35Q35, 35B65.


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  • [1]

    C. J. Amick, Regularity and uniqueness of solutions to the boussinesq system of equations, J. Diff. Eq., 54 (1984), 231-247.


    T. B. Benjamin, "Lectures on Nonlinear Wave Motion," Lectures in Applied Mathematics, Vol. 15, Amer. Math. Soc., Providence, R.I., 1974.


    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.doi: doi:10.1017/S030500410005218X.


    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.doi: doi:10.1016/0022-247X(80)90098-0.


    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.doi: doi:10.1007/s00332-002-0466-4.


    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.doi: doi:10.1088/0951-7715/17/3/010.


    J. R. Cannon, "The One-dimensional Heat Equation," Encyclopedia of Mathematics and its Applications, 23, 1984.


    N. Dunford and J. Schwartz, "Linear Operators. Part I," Pure and Applied Mathematics, Vol. VII, Interscience Publishers, New York, 1988.


    A. S. Fokas and B. Pelloni, Boundary value problems for Boussinesq type systems, Math. Phys., Anal. Geom., 8 (2005), 59-96.doi: doi:10.1007/s11040-004-1650-6.


    A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice Hall, Englewood Cliffs, N.J. 1964.


    P. D. Lax, "Shock Waves and Entropy," in Contributions to Non-Linear Functionnal Analysis, Academic Press, 1971.


    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.


    W. Rudin, "Functionnal Analysis," McGraw-Hill, New York, 1973.


    M. E. Schonbek, Existence of solutions for the Boussinesq system of equations, J. Differential Equations, 42 (1981), 325-352.doi: doi:10.1016/0022-0396(81)90108-X.


    G. B. Whitham, "Linear and Nonlinear Waves," Pure and Applied Mathematics, Wiley-Interscience, New-York-London-Sydney, 1974.

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