References
- F. M. Christ and M. I. Weinstein. Dispersion of small amplitude solutions of the generalized Korteweg–de Vries equation. Journal of Functional Analysis, 100(1):87–109, 1991. http://dx.doi.org/10.1016/0022-1236(91)90103-C.
- G. M. Coclite and L. di Ruvo. Convergence of the Ostrovsky equation to the Ostrovsky–Hunter one. Journal of Differential Equations, 256(9):3245–3277, 2014. http://dx.doi.org/10.1016/j.jde.2014.02.001.
- G. M. Coclite and L. di Ruvo. Convergence of the Kuramoto-Sinelshchikov equation to the Burges one. Acta Appl. Math., 2016.
- G. M. Coclite and L. di Ruvo. A note on the convergence of the solutions of the Camassa–Holm equation to the entropy ones of a scalar conservation law. Discrete and Continuous Dynamical Systems, 36(6):2981–2990, 2016. http://dx.doi.org/10.3934/dcds.2016.36.2981.
- G. M. Coclite and L. di Ruvo. Singular limit problem for conservation laws related to the Kawahara equation. Bull. Sci. Math., 2016.
- G. M. Coclite and L. di Ruvo. Singular limit problem for conservation laws related to the Kawahara Korteweg–de Vries equation. Netw. Heterog. Media., 2016.
- G. M. Coclite and K.H. Karlsen. A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation. Communications in Partial Differential Equations, 31(8):1253–1272, 2006. http://dx.doi.org/10.1080/03605300600781600.
- A. Cohen. Existence and regularity for solutions of the Korteweg–de Vries equation. Archive for Rational Mechanics and Analysis, 71(2):143–175, 1979. http://dx.doi.org/10.1007/BF00248725.
- R. Cˆote. Large data wave operator for the generalized Korteweg–de Vries equations. Differential Integral Equations, 19(2):163–188, 2006.
- C. de Lellis, F. Otto and M. Westdickenberg. Minimal entropy conditions for Burgers equation. Quarterly Applied Mathematics, 62(4):687–700, 2004.
- C. Foias, B. Nicolaenko, G.R. Sell and R. Temam. Inertial manifolds for the Kuramoto–Sivashinsky equation and an estimate of their lowest dimension. Journal de Mathematiques Pures et Appliquees, 67(3):197–226, 1988.
- D. J. Korteweg and G. de Vries.XLI. on the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philosophical Magazine Series 5, 39(240):422–443, 1895. http://dx.doi.org/10.1080/14786449508620739.
- Y. Kuramoto. Diffusion–induced chaos in reaction systems. Progress of Theoretical Physics Supplement, 64:346–367, 1978. http://dx.doi.org/10.1143/PTPS.64.346.
- Y. Kuramoto and T. Tsuzuki. On the formation of dissipative structures in reaction–diffusion systems: Reductive perturbation approach. Progress of Theoretical Physics, 54(3):687–699, 1975. http://dx.doi.org/10.1143/PTP.54.687.
- Y. Kuramoto and T. Tsuzuki. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Progress of Theoretical Physics, 55(2):356–369, 1976. http://dx.doi.org/10.1143/PTP.55.356.
- P. Lax and C.D. Levermore. The zero dispersion limit for the Korteweg de Vries KdV equation. Proceedings of the National Academy of Sciences, 76(8):3602– 3606, 1979.
- P. G. LeFloch and R. Natalini. Conservation laws with vanishing nonlinear diffusion and dispersion. Nonlinear Analysis: Theory, Methods & Applications, 36(2):213–230, 1999. http://dx.doi.org/10.1016/S0362-546X(98)00012-1.
- F. Murat. L'injection du cˆone positif de H−1 dans W −1, q est compacte pourtout q < 2. J. Math. Pures Appl. (9), 60(3):309–322, 1981.
- B. Nicolaenko and B. Scheurer. Remarks on the Kuramoto–Sivashinsky equation. Physica D: Nonlinear Phenomena, 12(1):391–395, 1984. http://dx.doi.org/10.1016/0167-2789(84)90543-8.
- B. Nicolaenko, B. Scheurer and R. Temam. Some global dynamical properties of the Kuramoto–Sivashinsky equations: nonlinear stability and attractors. Physica D: Nonlinear Phenomena, 16(2):155–183, 1985. http://dx.doi.org/10.1016/0167-2789(85)90056-9.
- M. E. Schonbek. Convergence of solutions to nonlinear dispersive equations. Communications in Partial Differential Equations, 7(8):959–1000, 1982. http://dx.doi.org/10.1080/03605308208820242.
- G. I. Sivashinsky. Nonlinear analysis of hydrodynamic instability in laminar flames – i. derivation of basic equations. Acta Astronautica, 4(11):1177–1206, 1977. http://dx.doi.org/10.1016/0094-5765(77)90096-0.