Asymptotic behaviors of radially symmetric solutions of \(\square u=| u| ^ p\) for super critical values \(p\) in odd space dimensions
type: Item
instance of: scholarly article
title: Asymptotic behaviors of radially symmetric solutions of \(\square u=| u| ^ p\) for super critical values \(p\) in odd space dimensions
zbMATH Open document ID: 0840.35063
author: Hideo Kubo
author: Kôji Kubota
published in: Hokkaido Mathematical Journal
publication date: 1995-10-23T00:00:00Z
review text: Semilinear wave equations \(u_{tt}- \Delta u= F(u)\) in \(x\in \mathbb{R}^n\), \(t\in \mathbb{R}\), where typically \(F(u)= |u|^p\) or \(F(u)= |u|^{p- 1}u\) with \(p> 1\), \(n\geq 2\) are considered. If \(p\) is larger than the positive root of \({n- 1\over 2} p^2- {n+ 1\over 2} p- 1= 0\) and \(p\leq {n+ 1\over n- 3}\) if \(n\geq 7\), global radially symmetric small solutions are shown to exist as well as the scattering operator, provided \(n\geq 5\) and \(n\) is odd.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 808299
zbMATH Keywords: semilinear wave equations
zbMATH Keywords: global radially symmetric small solutions
reviewed by: Reinhard Racke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1380892596
OpenAlex ID: W2059974869
DOI: 10.14492/HOKMJ/1380892596
description: scientific article; zbMATH DE number 808299