Author
Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date
2023
Publication Place
-
Taylor and Francis
Subject
35A35, 35C20, 35E15, 35Q53, Approximation, Benjamin–Bona–Mahony equation, Long wave limit, Non-local wave equation, Rosenau equation
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0003-6811
Record ID
0ea2a537-3e3e-451d-8518-43775a2fc2c3
Library Location
Natural and Mathematical Sciences
Date
2023
Sample Text
In this work, we prove a comparison result for a general class of nonlinear dispersive unidirectional wave equations. The dispersive nature of one-dimensional waves occurs because of a convolution integral in space. For two specific choices of the kernel function, the Benjamin–Bona–Mahony equation and the Rosenau equation that are particularly suitable to model water waves and elastic waves, respectively, are two members of the class. We first prove an energy estimate for the Cauchy problem of the non-local unidirectional wave equation. Then, for the same initial data, we consider two distinct solutions corresponding to two different kernel functions. Our main result is that the difference between the solutions remains small in a suitable Sobolev norm if the two kernel functions have similar dispersive characteristics in the long-wave limit. As a sample case of this comparison result, we provide the approximations of the hyperbolic conservation law.
DOI
10.1080/00036811.2022.2118117
Cilt
102
