# American Institute of Mathematical Sciences

November  2013, 33(11&12): 5293-5303. doi: 10.3934/dcds.2013.33.5293

## How to distinguish a local semigroup from a global semigroup

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

Received  September 2011 Revised  March 2012 Published  May 2013

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..
Citation: J. W. Neuberger. How to distinguish a local semigroup from a global semigroup. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 5293-5303. doi: 10.3934/dcds.2013.33.5293
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