Optimal decay rates of the dissipative shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation with power of nonlinearity

作者：

Highlights：

• This paper studies the asymptotic behavior of a solution of dispersive shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation.

• The energy decay rates of the solution to the model are examined through the Fourier transform method.

• The existence and uniqueness of numerical solutions are guaranteed while the convergence and stability are verified.

• The spatial accuracy is analyzed and found to be second-order on a uniform grid.

摘要

•This paper studies the asymptotic behavior of a solution of dispersive shallow water waves modeled by coupling the Rosenau-RLW equation and the Rosenau-Burgers equation.•The energy decay rates of the solution to the model are examined through the Fourier transform method.•The existence and uniqueness of numerical solutions are guaranteed while the convergence and stability are verified.•The spatial accuracy is analyzed and found to be second-order on a uniform grid.

论文关键词：Rosenau-RLW equation,Rosenau-Burgers equation,Large-time behaviour,Pseudo-compact finite difference scheme

论文评审过程：Received 28 May 2020, Revised 25 January 2021, Accepted 14 March 2021, Available online 22 April 2021, Version of Record 22 April 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126202