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Asymptotic Expansion of the Solutions to a Regularized Boussinesq System (Theory and Numerics).
- Source :
-
Acta Applicandae Mathematicae . 6/3/2024, Vol. 191 Issue 1, p1-25. 25p. - Publication Year :
- 2024
-
Abstract
- We consider the propagation of surface water waves described by the Boussinesq system. Following (Molinet et al. in Nonlinearity 34:744–775, 2021), we introduce a regularized Boussinesq system obtained by adding a non-local pseudo-differential operator define by g λ [ ζ ] ˆ = | k | λ ζ ˆ k 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 numerically the function coefficients of the expansion (in ϵ ) and verify numerically the validity of this expansion up to order 2. We also check the numerical L 2 stability of the numerical algorithm. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ASYMPTOTIC expansions
*PSEUDODIFFERENTIAL operators
*WATER waves
Subjects
Details
- Language :
- English
- ISSN :
- 01678019
- Volume :
- 191
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Acta Applicandae Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 177625503
- Full Text :
- https://doi.org/10.1007/s10440-024-00660-3