Scattering operator for semirelativistic Hartree type equation with a short range potential.
type: Item
instance of: scholarly article
title: Scattering operator for semirelativistic Hartree type equation with a short range potential.
zbMATH Open document ID: 1374.35330
author: Nakao Hayashi
author: Pavel I. Naumkin
author: Takayoshi Ogawa
published in: Differential and Integral Equations
publication date: 2015-09-29T00:00:00Z
review text: Based on the authors' abstract: In this paper, the authors showed the existence of the scattering operator in the neighborhood of the origin in \(H^{\omega ,1}\cap H^{\mu}\), where \(\mu >\omega =1+\frac2n\) for the semirelativistic Hartree type equation \[ i\partial_tu=\sqrt{M^2-\Delta}u+F(u),\quad (t,x)\in\mathbb{R}\times\mathbb{R}^n, \] where \(F(u)=(|x|^{-\gamma} \ast |u|^2)u\), \(1<\gamma <2\), \(n\geq 3\) and \(\ast\) denotes the convolution.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 6486987
zbMATH Keywords: semirelativistic Hartree type equation
zbMATH Keywords: final state problem
zbMATH Keywords: scattering
zbMATH Keywords: convolution
reviewed by: Guixiang Xu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6486987