Blow-up and critical exponents for nonlinear hyperbolic equations
type: Item
instance of: scholarly article
title: Blow-up and critical exponents for nonlinear hyperbolic equations
zbMATH Open document ID: 1012.35058
DOI: 10.1016/S0362-546X(02)00311-5
author: V. A. Galaktionov
author: S. I. Pokhozhaev
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-04-27T00:00:00Z
review text: From authors' abstract: We prove nonexistence results for the Cauchy problem for an abstract hyperbolic equation in a Banach space. Several applications to the second- and higher-order hyperbolic equations with local and nonlocal nonlinearities are presented. We also describe an approach to Kato's and John's critical exponents for the semilinear equations \(u_{t}=\triangle u+b(x,t)|u|^{p}\), \(p>1,\) which are responsible for phenomena of stability, instability, blow-up and asymptotic behaviour.
Mathematics Subject Classification ID: 35L90
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1900943
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: nonexistence results
zbMATH Keywords: energy estimate
zbMATH Keywords: abstract hyperbolic equation in a Banach space
zbMATH Keywords: local nonlinearity
zbMATH Keywords: nonlocal nonlinearity
zbMATH Keywords: stability
zbMATH Keywords: instability
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1900943