Blow-up for nonlinear wave equations with slowly decaying data
type: Item
instance of: scholarly article
title: Blow-up for nonlinear wave equations with slowly decaying data
zbMATH Open document ID: 0814.35077
DOI: 10.1007/BF02571961
author: H. Takamura
published in: Mathematische Zeitschrift
publication date: 1995-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/174707
review text: We consider classical solutions to the initial value problem for the ``accretive'' equation \(\square u = | u_ t |^ p\) in \(\mathbb{R}^ n \times [0, \infty)\) with ``small'' data. If the data have compact support, it is partially known that there is a number \(p_ 0(n)\) such that solutions blow-up in finite time for \(1< p \leq p_ 0 (n)\) and a global solution exists for \(p > p_ 0(n)\). In this paper, we shall show for \(n = 4,5\) that, if the support of data is noncompact, there are blowing-up solutions even for \(p > p_ 0 (n)\) because of the ``bad'' spatial decay of the initial data.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 737154
zbMATH Keywords: slowly decaying data
zbMATH Keywords: nonlinear wave equation
zbMATH Keywords: blow-up
reviewed by: Hiroki Takamura
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 737154