Comptes Rendus
Partial Differential Equations
Existence of local strong solutions for a quasilinear Benney system
[Existence d'une solution locale forte pour un système de Benney quasilinéaire]
Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 493-496.

Nous prouvons dans cette Note l'existence et unicité d'une solution locale forte du problème de Cauchy pour le 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.03.005

João-Paulo Dias 1 ; Mário Figueira 1 ; Filipe Oliveira 2

1 CMAF/UL and FCUL, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
2 Dep. Matemática, FCT/UNL, Monte da Caparica, Portugal
@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  - 
%0 Journal Article
%A João-Paulo Dias
%A Mário Figueira
%A Filipe Oliveira
%T Existence of local strong solutions for a quasilinear Benney system
%J Comptes Rendus. Mathématique
%D 2007
%P 493-496
%V 344
%N 8
%I Elsevier
%R 10.1016/j.crma.2007.03.005
%G en
%F CRMATH_2007__344_8_493_0
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] D.J. Benney 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] T. Kato Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Math., vol. 448, Springer, 1975, pp. 25-70

[4] F. Oliveira Stability of the solitons for the one-dimensional Zakharov–Rubenchik equation, Physica D, Volume 175 (2003), pp. 220-240

[5] Y. Shibata; Y. Tsutsumi Local existence of solutions for the initial boundary problem of fully nonlinear wave equation, Nonlinear Anal. TMA, Volume 11 (1987), pp. 335-365

[6] M. Tsutsumi; S. Hatano Well-posedness of the Cauchy problem for the long wave–short wave resonance equations, Nonlinear Anal. TMA, Volume 22 (1994), pp. 155-171

[7] M. Tsutsumi; S. Hatano 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

Cité par Sources :

Commentaires - Politique