How to distinguish a local semigroup from a global semigroup

J. W. Neuberger

doi:10.3934/dcds.2013.33.5293

Article Contents

2013, Volume 33, Issue 11&12: 5293-5303. Doi: 10.3934/dcds.2013.33.5293

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How to distinguish a local semigroup from a global semigroup

J. W. Neuberger^1,

1.
Department of Mathematics, University of North Texas, Denton, TX 76205-5017

Received: September 2011

Revised: March 2012

Published: November 2013

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Abstract

For a given autonomous time-dependent system that generates either a global, in time, semigroup or else only a local, in time, semigroup, a test involving a linear eigenvalue problem is given which determines which of `global' or `local' holds. Numerical examples are given. A linear transformation $A$ is defined so that one has `global' or `local' depending on whether $A$ does not or does have a positive eigenvalue. There is a possible application to Navier-Stokes problems..

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Mathematics Subject Classification: Primary: 47H20; Secondary: 47N99.

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