Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation
作者： Jerry L. Bona , Vassilios A. Dougalis , Ohannes A. Karakashian , William R. McKinney
DOI: 10.1016/0168-9274(92)90049-J
关键词:
摘要: Abstract A numerical scheme is suggested, discussed, and implemented for the approximation of solutions to periodic initial-value problem generalized Korteweg-de Vries-Burgers equation. The resulting computer code used study singularity formation other aspects interaction between nonlinearity, dispersion, dissipation that hallmark these evolutionary equations. It found unless coefficient specifying strength large enough, initial data may lead lose smoothness in finite time exactly same way as do dissipationless
elsevier.com
sci-hub.se 参考文章(17)
Jerry L Bona, Panagiotis E Souganidis, Walter A Strauss, Stability and Instability of Solitary Waves of Korteweg-de Vries Type Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 411, pp. 395- 412 ,(1987) , 10.1098/RSPA.1987.0073
Jerry L. Bona, Vassilios A. Dougalis, Ohannes A. Karakashian, Fully discrete galerkin methods for the korteweg-de vries equation☆ Computers & Mathematics With Applications. ,vol. 12, pp. 859- 884 ,(1986) , 10.1016/0898-1221(86)90031-3
Ohannes Karakashian, William McKinney, On optimal high-order in time approximations for the Korteweg-de Vries equation Mathematics of Computation. ,vol. 55, pp. 473- 496 ,(1990) , 10.1090/S0025-5718-1990-1035935-4
Model Equations for Long Waves in Nonlinear Dispersive Systems Philosophical Transactions of the Royal Society A. ,vol. 272, pp. 47- 78 ,(1972) , 10.1098/RSTA.1972.0032
L. Abdelouhab, J.L. Bona, M. Felland, J.-C. Saut, Nonlocal models for nonlinear, dispersive waves Physica D: Nonlinear Phenomena. ,vol. 40, pp. 360- 392 ,(1990) , 10.1016/0167-2789(89)90050-X
Garth A. Baker, Vassilios A. Dougalis, Ohannes A. Karakashian, Convergence of Galerkin Approximations for the Korteweg-de Vries Equation, Mathematics of Computation. ,vol. 40, pp. 419- 433 ,(1983) , 10.1090/S0025-5718-1983-0689464-4
R. S. Johnson, A non-linear equation incorporating damping and dispersion Journal of Fluid Mechanics. ,vol. 42, pp. 49- 60 ,(1970) , 10.1017/S0022112070001064
Harold Grad, Unified Shock Profile in a Plasma Physics of Fluids. ,vol. 10, pp. 2596- 2602 ,(1967) , 10.1063/1.1762081
R. S. Johnson, Shallow Water Waves on a Viscous Fluid—The Undular Bore Physics of Fluids. ,vol. 15, pp. 1693- 1699 ,(1972) , 10.1063/1.1693764
C.J Amick, J.L Bona, M.E Schonbek, Decay of solutions of some nonlinear wave equations Journal of Differential Equations. ,vol. 81, pp. 1- 49 ,(1989) , 10.1016/0022-0396(89)90176-9