Mathematical analysis of bump to bucket problem

Min Chen; Olivier Goubet; Shenghao Li

doi:10.3934/cpaa.2020251

Article Contents

2020, Volume 19, Issue 12: 5567-5580. Doi: 10.3934/cpaa.2020251

This issue Previous Article A truncated real interpolation method and characterizations of screened Sobolev spaces Next Article Lifespan of solutions to a fourth order parabolic PDE involving the Hessian modeling epitaxial growth

Mathematical analysis of bump to bucket problem

1.
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
2.
LAMFA UMR 7352 CNRS, Université de Picardie Jules Verne, 80039 Amiens CEDEX 1, France
3.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2020

Revised: June 30, 2020

Early access: October 2020

Published: December 2020

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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Abstract

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.

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

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