In this Note, it is shown that a Fourier Galerkin approximation of the Korteweg–de Vries equation with periodic boundary conditions converges exponentially fast if the initial data can be continued analytically to a strip about the real axis.
Dans cette Note, nous montrons que l'approximation donnée par une methode de Galerkin de type Fourier de l'équation de Korteweg–de Vries avec conditions aux bords périodiques converge de façon exponentielle si les donnes initiales peuvent être prolonges analytiquement sur une bande autour de l'axe réel.
Accepted:
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Henrik Kalisch 1
@article{CRMATH_2005__341_7_457_0, author = {Henrik Kalisch}, title = {Rapid convergence of a {Galerkin} projection of the {KdV} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {457--460}, publisher = {Elsevier}, volume = {341}, number = {7}, year = {2005}, doi = {10.1016/j.crma.2005.09.006}, language = {en}, }
Henrik Kalisch. Rapid convergence of a Galerkin projection of the KdV equation. Comptes Rendus. Mathématique, Volume 341 (2005) no. 7, pp. 457-460. doi : 10.1016/j.crma.2005.09.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.006/
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