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On the Differentiabilityof Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator

On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011 English Publisher:WileyJournal:International Journal of Mathematics and Mathematical Sciences, volume 2,011 (issn: 0161-1712, eissn: 1687-0425, Copyright policy )
Authors: Marat V. Markin;

doi: 10.1155/2011/825951

On the Differentiabilityof Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator

Abstract

For the evolution equation y′(t) = Ay(t) with a scalar type spectral operator A in a Banach space, conditions on A are found that are necessary and sufficient for all weak solutions of the equation on [0, ∞) to be strongly infinite differentiable on [0, ∞) or [0, ∞). Certain effects of smoothness improvement of the weak solutions are analyzed.

Related Organizations
Keywords

Linear differential equations in abstract spaces, QA1-939, Mathematics

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selected citations
These citations are derived from selected sources.
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!
1
Average
Average
Average
gold