Generalized solutions of the Benjamin-Ono and Smith equations
type: Item
instance of: scholarly article
title: Generalized solutions of the Benjamin-Ono and Smith equations
zbMATH Open document ID: 0809.35100
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-06-08T00:00:00Z
review text: Existence and uniqueness of solution of Cauchy problem for the Benjamin- Ono equation \(\partial_ t u=- \partial_ x(u^ 2+ 2\sigma\partial_ x u)\) and Smith equation \(\partial_ t u=- \partial_ x(u^ 2- 2Lu)\) are proved. Here \(\sigma\) denotes the Hilbert transform \[ (\sigma f)(x)= \text{p.v. } {1\over \pi} \int {{f(x')} \over {x'-x}} dx \] and \(L\) is the operator of the form \(Lf= ((-\partial_ x^ 2+ 1)^{1/2} -1)f\).
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 584067
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Benjamin-Ono equation
zbMATH Keywords: Smith equation
zbMATH Keywords: Hilbert transform
author: H. A. Biagioni
author: Rafael José jun. Iorio
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1098
OpenAlex ID: W1995373000
DOI: 10.1006/JMAA.1994.1098
description: scientific article; zbMATH DE number 584067