Asymptotic expansion of the solutions to a regularized Boussinesq system (theory and numeric)
Résumé
We here consider the propagation of surface water waves described by the Boussinesq system. Following [9], we introduce a regularized Boussinesq system obtained by adding a non-local pseudo-differential operator define by g λ [ζ] = |k| λ ζk with λ ∈]0, 2]. In this paper, we display a twofold approach: First, we study theoretically the existence of an asymptotic expansion for the solution to the Cauchy problem associated to this regularized Boussinesq system with respect to the regularizing parameter ϵ. Then, we compute the function coefficients of the expansion (in ϵ) numerically and verify numerically the validity of this expansion up to order 2. We also check the numerical L 2 stability of the numerical algorithm.
Mots clés
Boussinesq system Energy estimate Cauchy problem numerical stability numerical Fourier transform numerical expansion. Mathematics Subject Classification numbers: 35Q35 35L56 35B30 35B40 65T99
Boussinesq system
Energy estimate
Cauchy problem
numerical stability
numerical Fourier transform
numerical expansion. Mathematics Subject Classification numbers: 35Q35
35L56
35B30
35B40
65T99
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
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