Global nonexistence theorems for a class of evolution equations with dissipation
type: Item
instance of: scholarly article
title: Global nonexistence theorems for a class of evolution equations with dissipation
zbMATH Open document ID: 0934.35101
author: Enzo Vitillaro
published in: Archive for Rational Mechanics and Analysis
publication date: 2000-04-02T00:00:00Z
review text: The paper deals with the problem of non-continuation for a solution of the abstract evolution equation \( [P(u'(t))]'+A(u(t))+Q(t,u'(t))=F(u(t))\), \(t\in (0,T), \) satisfying given initial data, where \(A,F,P\) and \(Q\) are nonlinear operators on appropriate Banach spaces. Under specific assumptions on these operators, the author proves, that the solution cannot exist for all time in the case of certain initial data. The results are applicable to important dynamical problems of nonlinear equations of elasticity with nonlinear damping.
Mathematics Subject Classification ID: 35L90
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 1384882
zbMATH Keywords: non-continuation of a solution
zbMATH Keywords: abstract evolution equation
zbMATH Keywords: equations of elasticity with nonlinear damping
zbMATH Keywords: weak solution
reviewed by: Marie Kopáčková
MaRDI profile type: Publication
full work available at URL: s002050050171
OpenAlex ID: W2036608017
DOI: 10.1007/S002050050171
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description: scientific article; zbMATH DE number 1384882