Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions
type: Item
instance of: scholarly article
title: Global solutions and self-similar solutions of the coupled system of semilinear wave equations in three space dimensions
zbMATH Open document ID: 1016.35047
author: Hideo Kubo
author: Kotaro Tsugawa
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-08-04T00:00:00Z
review text: The authors treat the coupled system of wave equations \(u_{tt}-\triangle u=|u|^{p_1}|v|^{q_1}\), \(v_{tt}-\triangle v=|u|^{p_2}|v|^{q_2}\), \(x\in \mathbb{R}^n\), \(t>0.\) They give the lower bounds of \(p_j\), \(q_j\) to assure the global existence of a class of solutions including self-similar solutions for small initial data. If such conditions on \(p_j\), \(q_j\) are not satisfied, then no self-similar solution exists even for small data.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 1890749
zbMATH Keywords: coupled system of equations
zbMATH Keywords: self-similar solution
zbMATH Keywords: Cauchy problem
zbMATH Keywords: critical exponent
zbMATH Keywords: blow-up
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.471
OpenAlex ID: W1965935828
DOI: 10.3934/DCDS.2003.9.471
description: scientific article; zbMATH DE number 1890749