Global nonexistence for abstract evolution equations with positive initial energy
type: Item
instance of: scholarly article
title: Global nonexistence for abstract evolution equations with positive initial energy
zbMATH Open document ID: 0915.35012
author: Patrizia Pucci
author: James Serrin
published in: Journal of Differential Equations
publication date: 1999-06-23T00:00:00Z
review text: The authors consider the following initial value problem for abstract evolution equations \[ Pu_{tt}+Q(t)u_{t} +A(t,u)=F(t,u),\qquad t\in J=[0,\infty), \] with \(P\) and \(Q\) being linear self-adjoint operators, while \(A(t,u)\) and \(F(t,u)\) are, respectively, a linear operator in \(u\) and a nonlinear driving force. Introducing an appropriate coercive operator associated with the equation above, the authors prove noncontinuation (blow-up) of solutions when the initial energy is positive.
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B60
zbMATH DE Number: 1241039
zbMATH Keywords: abstract second-order evolution equation
zbMATH Keywords: noncontinuation of the solutions
zbMATH Keywords: blow up
reviewed by: Dian K. Palagachev
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3477
OpenAlex ID: W1968240705
cites work: Q4073917
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DOI: 10.1006/JDEQ.1998.3477
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description: scientific article; zbMATH DE number 1241039