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How to distinguish a local semigroup from a global semigroup

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


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