[Existence d'une solution locale forte pour un système de Benney quasilinéaire]
We prove in this Note the existence and uniqueness of a strong local solution to the Cauchy problem for the quasilinear Benney system.
Nous prouvons dans cette Note l'existence et unicité d'une solution locale forte du problème de Cauchy pour le système de Benney quasilinéaire.
Accepté le :
Publié le :
João-Paulo Dias 1 ; Mário Figueira 1 ; Filipe Oliveira 2
@article{CRMATH_2007__344_8_493_0,
author = {Jo\~ao-Paulo Dias and M\'ario Figueira and Filipe Oliveira},
title = {Existence of local strong solutions for a quasilinear {Benney} system},
journal = {Comptes Rendus. Math\'ematique},
pages = {493--496},
publisher = {Elsevier},
volume = {344},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.03.005},
language = {en},
}
TY - JOUR AU - João-Paulo Dias AU - Mário Figueira AU - Filipe Oliveira TI - Existence of local strong solutions for a quasilinear Benney system JO - Comptes Rendus. Mathématique PY - 2007 SP - 493 EP - 496 VL - 344 IS - 8 PB - Elsevier DO - 10.1016/j.crma.2007.03.005 LA - en ID - CRMATH_2007__344_8_493_0 ER -
João-Paulo Dias; Mário Figueira; Filipe Oliveira. Existence of local strong solutions for a quasilinear Benney system. Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 493-496. doi : 10.1016/j.crma.2007.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.005/
[1] A general theory for interactions between short and long waves, Stud. Appl. Math., Volume 56 (1977), pp. 81-94
[2] J.P. Dias, M. Figueira, Existence of weak solutions for a quasilinear version of Benney equations, J. Hyperbolic Differential Equations, in press
[3] Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Math., vol. 448, Springer, 1975, pp. 25-70
[4] Stability of the solitons for the one-dimensional Zakharov–Rubenchik equation, Physica D, Volume 175 (2003), pp. 220-240
[5] Local existence of solutions for the initial boundary problem of fully nonlinear wave equation, Nonlinear Anal. TMA, Volume 11 (1987), pp. 335-365
[6] Well-posedness of the Cauchy problem for the long wave–short wave resonance equations, Nonlinear Anal. TMA, Volume 22 (1994), pp. 155-171
[7] Well-posedness of the Cauchy problem for Benney's first equations of long wave short wave interactions, Funkcial. Ekvac., Volume 37 (1994), pp. 289-316
- A quasilinear system related with the asymptotic equation of the nematic liquid crystal's director field, Chinese Annals of Mathematics. Series B, Volume 42 (2021) no. 2, pp. 163-172 | DOI:10.1007/s11401-021-0251-z | Zbl:1475.35267
- Global existence and blow-up for the classical solutions of the long-short wave equations with viscosity, Discrete Dynamics in Nature and Society, Volume 2021 (2021), p. 16 (Id/No 7211126) | DOI:10.1155/2021/7211126 | Zbl:1486.35062
- On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law, Communications in Contemporary Mathematics, Volume 22 (2020) no. 7, p. 30 (Id/No 1950054) | DOI:10.1142/s0219199719500548 | Zbl:1446.35191
- Linear stability of shock profiles for a quasilinear Benney system in
- Decay of solutions for a class of nonlinear Schrödinger equations in
- On a quasilinear nonlocal Benney system, Journal of Hyperbolic Differential Equations, Volume 14 (2017) no. 1, pp. 135-156 | DOI:10.1142/s0219891617500047 | Zbl:1387.35562
- The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system, Journal of Dynamics and Differential Equations, Volume 25 (2013) no. 1, pp. 49-69 | DOI:10.1007/s10884-012-9283-0 | Zbl:1307.35271
- A nonlinear model describing a short wave – long wave interaction in a viscoelastic medium, Quarterly of Applied Mathematics, Volume 71 (2013) no. 3, pp. 417-432 | DOI:10.1090/s0033-569x-2012-01298-4 | Zbl:1275.35082
- On the Cauchy problem describing an electron-phonon interaction, Chinese Annals of Mathematics. Series B, Volume 32 (2011) no. 4, pp. 483-496 | DOI:10.1007/s11401-011-0663-2 | Zbl:1347.37128
- Non-existence of global solutions for a quasilinear Benney system, Journal of Mathematical Fluid Mechanics, Volume 13 (2011) no. 2, pp. 213-222 | DOI:10.1007/s00021-009-0014-1 | Zbl:1270.35358
- Erratum to: “Non-existence of global solutions for a quasilinear Benney system”, Journal of Mathematical Fluid Mechanics, Volume 13 (2011) no. 2, p. 307 | DOI:10.1007/s00021-009-0021-2 | Zbl:1270.35359
- Vanishing viscosity with short wave-long wave interactions for systems of conservation laws, Archive for Rational Mechanics and Analysis, Volume 196 (2010) no. 3, pp. 981-1010 | DOI:10.1007/s00205-009-0273-2 | Zbl:1203.35020
- Well-posedness and existence of bound states for a coupled Schrödinger-gKdV system, Nonlinear Analysis. Theory, Methods Applications. Series A: Theory and Methods, Volume 73 (2010) no. 8, pp. 2686-2698 | DOI:10.1016/j.na.2010.06.049 | Zbl:1194.35405
Cité par 13 documents. Sources : zbMATH
Commentaires - Politique