A note on existence of global classical solutions to nonlinear wave equations
type: Item
instance of: scholarly article
title: A note on existence of global classical solutions to nonlinear wave equations
zbMATH Open document ID: 0652.35076
DOI: 10.1007/BF02386113
published in: Arkiv för Matematik
publication date: 1988-01-01T00:00:00Z
review text: The author examines the semilinear wave equation \[ u_{tt}-\Delta u=t^{1-k}u\quad k,\quad x\in {\mathbb{R}}\quad 3,\quad t>0 \] with data \(u(x,0)=0\), \(u_ t(x,0)=g(x).\) For g(x) satisfying a growth condition related to the Lane-Emden equation of index \(k\geq 5\) and with g(x) smooth and positive, it is shown that there exists a classical global unique solution.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35L15
zbMATH DE Number: 4063673
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: growth condition
zbMATH Keywords: Lane-Emden equation
zbMATH Keywords: classical global unique solution
author: Peter Kumlin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4063673