Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
type: Item
instance of: scholarly article
title: Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
zbMATH Open document ID: 1056.35120
author: Ryo Ikehata
author: Yasuaki Miyaoka
author: Takashi Nakatake
published in: Journal of the Mathematical Society of Japan
publication date: 2004-10-27T00:00:00Z
review text: The paper deals with the Cauchy problem to the equation \(u_{tt}-\triangle u+u_t=| u| ^{p-1}u,\) \(t>0,\) \(x\in \mathbb R^n\) (\(n=1,2,3\)), where \(p\in (1+2/n,+\infty)\) for \(n=1,2\) and \(p\in (2,3]\) for \(n=3.\) If the initial data are sufficiently small, then the problem admits a global solution satisfying a decay property.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 2110887
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: global solution
zbMATH Keywords: small initial data
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1191418635
OpenAlex ID: W2030876627
DOI: 10.2969/JMSJ/1191418635
description: scientific article; zbMATH DE number 2110887