Sharp condition for global existence and blow-up on Klein-Gordon equation
type: Item
instance of: scholarly article
title: Sharp condition for global existence and blow-up on Klein-Gordon equation
zbMATH Open document ID: 1184.35073
DOI: 10.1155/2009/164303
author: Zhao Junsheng
author: Li Shufeng
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45798
review text: Summary: We study the initial boundary value problem of the nonlinear Klein-Gordon equation. First, we introduce a family of potential wells. By using them, we obtain a new existence theorem of global solutions and show the blow-up in finite time of solutions. Especially, the relation between the above two phenomena is derived as a sharp condition.
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 5632440
zbMATH Keywords: family of potential wells
Wikidata QID: Q58648887
MaRDI profile type: Publication
OpenAlex ID: W2031002938
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cites work: Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
cites work: Saddle points and instability of nonlinear hyperbolic equations
cites work: Q3925286
cites work: Q3995410
cites work: Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.
cites work: On potential wells and applications to semilinear hyperbolic equations and parabolic equations
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description: scientific article; zbMATH DE number 5632440