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Mathematical analysis of bump to bucket problem

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O. Goubet acknowledges the financial support of both SODDA research project funded by Region Hauts-de-France and FEDER from E.C., and S2R 2018 - Action 4.3 of UPJV. S. Li is supported by the Applied Fundamental Research Program of Sichuan Province (no. 2020YJ0264)

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  • In this article, several systems of equations which model surface water waves generated by a sudden bottom deformation (bump) are studied. Because the effect of such deformation are often approximated by assuming the initial water surface has a deformation (bucket), this procedure is investigated and we prove rigorously that by using the correct bucket, the solutions of the regularized bump problems converge to the solution of the bucket problem.

    Mathematics Subject Classification: Primary: 35Q35, 35Q53.


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