On some evolution inequalities in a Hilbert space
type: Item
instance of: scholarly article
title: On some evolution inequalities in a Hilbert space
zbMATH Open document ID: 0961.34051
author: B. G. Pachpatte
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-05-16T00:00:00Z
review text: In this -- rather technical note -- the author gives some evolution inequalities related to Sobolev type evolution equations. Such inequalities are used to study the uniqueness and asymptotic growth of solutions to differential inequalities of the form \[ \|B(t)u'(t) - A(t)u(t)\|\leq F(t,p(t),q(t)) \] and \[ \|B(t)u'(t) + M(t)u(t) - A(t)u(t)\|\leq G(t,p(t),q(t)), \] where \(B(t)\), \(A(t)\), \(M(t)\) are linear operators acting on a Hilbert space and \(p\), \(q\) , \(F\), \(G\) are suitable functions.
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 34A40
zbMATH DE Number: 1496346
zbMATH Keywords: Hilbert space
zbMATH Keywords: evolution inequalities
zbMATH Keywords: evolution equations of Sobolev type
reviewed by: Józef Myjak
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6767
OpenAlex ID: W1982906339
cites work: Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space
cites work: A semilinear Sobolev evolution equation in a Banach space
cites work: Q5630031
cites work: Q4744610
cites work: Lower bounds and uniqueness for solutions of evolution inequalities in a Hilbert space
cites work: Q5569338
cites work: Asymptotic Behaviour of Solutions of Parabolic Differential Inequalities
cites work: Logarithmic Convexity, First Order Differential Inequalities and Some Applications
cites work: A partial functional differential equation of Sobolev type
cites work: Decay of solutions of some nonlinear evolution equations
cites work: Lower Bounds for Solutions of Parabolic Differential Inequalities
cites work: On the maximum rate of decay of solutions of parabolic differential inequalities
cites work: Properties of Solutions of Parabolic Equations and Inequalities
cites work: Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach Space
cites work: Q4139057
DOI: 10.1006/JMAA.2000.6767
Recommended article: Nonlinear variational evolution inequalities in Hilbert spaces
Recommended article: Q4284715
Recommended article: Q4550447
Recommended article: Q3485314
Recommended article: Harnack-Type Inequalities for Evolution Equations
Recommended article: Evolution equations of Lurie-type in Hilbert spaces
Recommended article: Some existence theorems for evolution hemivariational inequalities
Recommended article: Q3974641
Recommended article: A class of generalized evolution variational inequalities in Banach spaces
Recommended article: Q3327030
description: scientific article; zbMATH DE number 1496346