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Preprint . 2006
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Mathematical Methods in the Applied Sciences
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Article . 2006
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On a class of PDEs with nonlinear distributed in space and time state‐dependent delay terms

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Jan 2008Embargo end date: 01 Jan 2006 English Publisher:WileyJournal:Mathematical Methods in the Applied Sciences, volume 31, pages 1,569-1,585 (issn: 0170-4214, eissn: 1099-1476, Copyright policy )
Authors: Alexander V. Rezounenko;

doi: 10.1002/mma.986 , 10.48550/arxiv.math/0611653

arXiv: http://arxiv.org/abs/math/0611653

On a class of PDEs with nonlinear distributed in space and time state‐dependent delay terms

Abstract

AbstractA new class of nonlinear partial differential equations with distributed in space and time state‐dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state‐dependent delay and discuss advantages of this class. Local and long‐time asymptotic properties, including the existence of global attractor and a principle of linearized stability, are studied. Copyright © 2008 John Wiley & Sons, Ltd.

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Keywords

Mathematics - Analysis of PDEs, FOS: Mathematics, Dynamical Systems (math.DS), 35R10, 35B41, 35K57, Mathematics - Dynamical Systems, Analysis of PDEs (math.AP)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green