A comparison of solutions of two convolution-type unidirectional wave equations

Name: A comparison of solutions of two convolution-type unidirectional wave equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	A comparison of solutions of two convolution-type unidirectional wave equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2023
Basım Yeri	- Taylor and Francis
Konu	35A35, 35C20, 35E15, 35Q53, Approximation, Benjamin–Bona–Mahony equation, Long wave limit, Non-local wave equation, Rosenau equation
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0003-6811
Kayıt Numarası	0ea2a537-3e3e-451d-8518-43775a2fc2c3
Lokasyon	Natural and Mathematical Sciences
Tarih	2023
Örnek Metin	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

Kaynağa git Özyeğin Üniversitesi

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Özyeğin Üniversitesi

Kaynağa git

A comparison of solutions of two convolution-type unidirectional wave equations

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2023

Basım Yeri - Taylor and Francis

Konu 35A35, 35C20, 35E15, 35Q53, Approximation, Benjamin–Bona–Mahony equation, Long wave limit, Non-local wave equation, Rosenau equation

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0003-6811

Kayıt Numarası 0ea2a537-3e3e-451d-8518-43775a2fc2c3

Lokasyon Natural and Mathematical Sciences

Tarih 2023

Örnek Metin 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