Zero-dissipation limit for nonlinear waves
ESAIM: Modélisation mathématique et analyse numérique, Special Issue for R. Temam's 60th birthday, Tome 34 (2000) no. 2, pp. 275-301.
@article{M2AN_2000__34_2_275_0,
     author = {Bona, Jerry L. and Wu, Jiahong},
     title = {Zero-dissipation limit for nonlinear waves},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {275--301},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {2},
     year = {2000},
     mrnumber = {1765660},
     zbl = {0953.76006},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_2_275_0/}
}
TY  - JOUR
AU  - Bona, Jerry L.
AU  - Wu, Jiahong
TI  - Zero-dissipation limit for nonlinear waves
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2000
SP  - 275
EP  - 301
VL  - 34
IS  - 2
PB  - Dunod
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_2000__34_2_275_0/
LA  - en
ID  - M2AN_2000__34_2_275_0
ER  - 
%0 Journal Article
%A Bona, Jerry L.
%A Wu, Jiahong
%T Zero-dissipation limit for nonlinear waves
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2000
%P 275-301
%V 34
%N 2
%I Dunod
%C Paris
%U http://www.numdam.org/item/M2AN_2000__34_2_275_0/
%G en
%F M2AN_2000__34_2_275_0
Bona, Jerry L.; Wu, Jiahong. Zero-dissipation limit for nonlinear waves. ESAIM: Modélisation mathématique et analyse numérique, Special Issue for R. Temam's 60th birthday, Tome 34 (2000) no. 2, pp. 275-301. http://www.numdam.org/item/M2AN_2000__34_2_275_0/

[1] L. Abdelouhab, J.L. Bona, M. Felland and J.-C. Saut, Non-local models for nonlinear, dispersive waves. Physica D 40 (1989) 360-392. | MR | Zbl

[2] C.J. Amick, J.L. Bona and M.E. Schonbek, Decay of solutions of some nonlinear wave equations. J. Differential Equations 81 (1989) 1-49. | MR | Zbl

[3] T.B. Benjamin, J.L. Bona and J.J. Mahony, Model equations for long waves in nonlinear Systems. Philos. Trans. Royal Soc. London Ser. A 272 (1972) 47-78. | MR | Zbl

[4] P. Biler, Asymptotic behavior in time of some equations generalizing the Korteweg-de Vries equation. Bull. Polish Acad. Sci. 32 (1984) 275-282. | MR | Zbl

[5] J.L. Bona, On solitary waves and their role in the evolution of long waves. In Applications of Nonlinear Analysis in the Physical Sciences, H. Amann, N. Bazley and K. Kirchgâssner Eds, Pitman, London (1983) 183=205. | Zbl

[6] J.L. Bona and P.J. Bryant, A mathematical model for long waves generated by a wave-maker in nonlinear dispersive Systems. Proc. Cambridge Philos. Soc. 73 (1973) 391-405. | MR | Zbl

[7] J.L. Bona, F. Demengel and K. Promislow, Fourier splitting and the dissipation of nonlinear waves. Proc. Royal Soc. Edinburgh 129A (1999) 477-502. | MR | Zbl

[8] J.L. Bona, V.A. Dougalis, O.A. Karakashian and W.R. Mckinney, The effect of dissipation on solutions of the generalized KdV equation. J. Comp. Appl. Math. 74 (1996) 127-154. | MR | Zbl

[9] J.L. Bona, V.A. Dougalis, O.A. Karakashian and W.R. Mckinney, Conservative high-order numerical schemes for the generalized Korteweg-de Vries equation. Philos. Trans. Poyal Soc. Lond. Ser. A 351 (1995) 107-164. | MR | Zbl

[10] J.L. Bona and L. Luo, Initial-boundary-value problems for model equations for the propagation of long waves. In Evolution Equations, G. Ferreyra, G.R. Goldstein, and F. Neubrander Eds, Marcel Dekker, Inc.: New York (1995) 65-94. | MR | Zbl

[11] J.L. Bona and L. Luo, A generalized Korteweg-de Vries equation in a quarter plane. Contemporary Math. 221 (1999) 59-125. | MR | Zbl

[12] J.L. Bona and L. Luo, Decay of solutions to nonlinear, dispersive, dissipative wave equations. Diff. & Intégral Equ. 6 (1993) 961-980. | MR | Zbl

[13] J.L. Bona and L. Luo, More results on the decay of solutions to nonlinear, dispersive wave equations. Discrete & Cont. Dynamical Systems 1 (1995) 151-193. | MR | Zbl

[14] J.L. Bona, W.G. Pritchard and L.R. Scott, An évaluation of a model equation for water waves. Philos. Trans. Royal Soc. Lond. Ser. A 302 (1981) 457-510. | MR | Zbl

[15] J.L. Bona, K. Promislow and C. E. Wayne, On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations. Math. & Computers in Simulation 37 (1994) 265-277. | MR | Zbl

[16] J.L. Bona, K. Promislow and C. E. Wayne, Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations. Nonlinearity 8 (1995) 1179-1206. | MR | Zbl

[17] J.L. Bona and R. Smith, The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Royal Soc. Lond. Ser. A 278 (1975) 555-601. | MR | Zbl

[18] J.L. Bona and R. Winther, The KdV equation, posed in a quarter plane. SIAM J. Math. Anal. 14 (1983) 1056-1106. | MR | Zbl

[19] J.L. Bona and R. Winther, KdV equation in a quarter plane, continuous dependence results. Diff. & Integral Equ. 2 (1989) 228-250. | MR | Zbl

[20] J.L. Bona and F.B. Weissler, Similarity solutions of the generalized Korteweg-de Vries equation. Math. Proc. Cambridge Philos. Soc. 127 (1999) 323-351. | MR | Zbl

[21] D. Dix, The dissipation of nonlinear dispersive waves. Comm. PDE 17 (1992) 1665-1693. | MR | Zbl

[22] R.S. Johnson, A nonlinear equation incorporating damping and dispersion. J. Fluid Mech. 42 (1970) 49-60. | MR | Zbl

[23] R.S. Johnson, Shallow water waves on a viscous fluid - The undular bore. Phys. Fluids 15 (1972) 1693-1699. | Zbl

[24] C. E. Kenig, G. Ponce and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. XLVI (1993) 27-94. | MR | Zbl

[25] C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation. J. Amer. Math. Soc. 9 (1996) 573-603. | MR | Zbl

[26] R.M. Miura, C.S. Gardner and M.D. Kruskal, Korteweg-de Vries equation and generalizations. II. Existence of conservation laws and constants of motion. J. Math. Phys. 9 (1968) 1204-1209. | MR | Zbl

[27] P. Naumkin andI. Shishmarev, Nonlinear nonlocal equations in the theory of waves. Series Translations of Math. Mono. 133, American Math. Soc.: Providence (1994). | MR | Zbl

[28] L.A. Ostrovsky, Short-wave asymptotics of weak shock waves and solitons in mechanics., Internat. J. Non-linear Mech. 11 (1976) 401-406. | MR | Zbl

[29] E. Ott and R.N. Sudan, Nonlinear theory of ion acoustic waves with Landau damping. Phys. Fluids 12 (1969) 2388-2394. | MR | Zbl

[30] J.-C. Saut, , Sur quelques géneralisations de l'équation de Korteweg-de Vries. J. Math. Pures Appl. 58 (1979) 21-61. | MR | Zbl

[31] J. Wu, , The inviscid limit of the complex Ginzburg-Landau equation. J. Differential Equations 142 (1998) 413-433. | MR | Zbl

[32] N.J. Zabusky and C.J. Galvin, Shallow-water waves, the KdV equation and solitons. J. Fluid Mech. 47 (1971) 811-824.

[33] B.-Y. Shang, , Taylor series expansion for solutions of the KdV equation with respect to their initial values. J. Funct. Anal. 129 (1995) 293-324. | MR | Zbl