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Existence of solutions for a Boussinesq system on the half line and on a finite interval
1. | Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, CNRS UMR 8628, 91405 Orsay, France |
References:
[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.
doi: doi:10.1017/S030500410005218X. |
[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.
doi: doi:10.1016/0022-247X(80)90098-0. |
[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.
doi: doi:10.1007/s00332-002-0466-4. |
[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.
doi: doi:10.1088/0951-7715/17/3/010. |
[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.
doi: doi:10.1007/s11040-004-1650-6. |
[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.
doi: doi:10.1016/0022-0396(81)90108-X. |
[15] |
G. B. Whitham, "Linear and Nonlinear Waves," Pure and Applied Mathematics, Wiley-Interscience, New-York-London-Sydney, 1974. |
show all references
References:
[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.
doi: doi:10.1017/S030500410005218X. |
[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.
doi: doi:10.1016/0022-247X(80)90098-0. |
[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.
doi: doi:10.1007/s00332-002-0466-4. |
[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.
doi: doi:10.1088/0951-7715/17/3/010. |
[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.
doi: doi:10.1007/s11040-004-1650-6. |
[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.
doi: doi:10.1016/0022-0396(81)90108-X. |
[15] |
G. B. Whitham, "Linear and Nonlinear Waves," Pure and Applied Mathematics, Wiley-Interscience, New-York-London-Sydney, 1974. |
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