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Remarks on the Korteweg-de Vries equation. (English) Zbl 0334.35062


MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35G25 Initial value problems for nonlinear higher-order PDEs
35B20 Perturbations in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
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References:

[1] C. Bardos, U. Frisch, P. Penel, P. L. Sulem (to appear).
[2] T. B. Benjamin,Lectures on Non-Linear Wave Motion: Lectures in Applied Mathematics, No. 15, Amer. Math. Soc., 1974.
[3] J. Bona, R. Scott,Solutions of the K. d. V. equation in fractional order Sobolev spaces, Duke Math. J. (to appear). · Zbl 0335.35032
[4] Bona, J.; Smith, R. S., The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London, 278, 555-604 (1975) · Zbl 0306.35027 · doi:10.1098/rsta.1975.0035
[5] Dushane,Generalizations of the Korteweg-de Vries equation, Proc. Symp. in Pure Math.23 (1971). · Zbl 0268.35072
[6] T. Kato,Quasilinear equations of evolution, with applications to partial differential equations, inSpectral theory and differential equations: Lecture Notes in Mathematics, Vol. 448, Springer-Verlag, 1974.
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[8] Lax, P. D., Periodic solutions of the K. d. V. equations, Comm. Pure Appl. Math., 28, 141-188 (1975) · Zbl 0295.35004 · doi:10.1002/cpa.3160280105
[9] Saut, J. C., Applications de l’interpolation non linéaire à des problèmes d’évolution non linéaires, J. Math. Pures Appl., 9, 27-52 (1974) · Zbl 0286.35057
[10] Saut, J. C., Sur certaines généralisations de l’équation de Korteweg-de Vries, C. R. Acad. Sc. Paris, 280, 653-656 (1975) · Zbl 0296.35018
[11] Strauss, W. A., On the regularity of functions with values in various Banach spaces, Pacific J. Math., 19, 543-551 (1966) · Zbl 0185.20103
[12] Tartar, L., Interpolation non linéaire et régularité, J. Functional Analysis, 9, 469-489 (1972) · Zbl 0241.46035 · doi:10.1016/0022-1236(72)90022-5
[13] Temam, R., Sur un problème non linéaire, J. Math. Pures Appl., 48, 159-172 (1969) · Zbl 0187.03902
[14] R. Temam,Proceedings on a Conference on Mathematical Problems in Turbulence: Lecture Notes in Mathematics, Springer-Verlag (to appear).
[15] Tsutsumi, M.; Mukasa, T., Parabolic regularizations for the generalized Korteweg-de Vries equation, Funkcial. Ekvac., 14, 89-110 (1971) · Zbl 0228.35077
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