Superstability and Finite Time Extinction For C_0-Semigroups

Details Superstability and Finite Time Extinction For C_0-Semigroups Superstability and Finite Time Extinction For C_0-Semigroups

2009-07-28

arxiv.org/abs/0907.4812v3

Mathematics

Functional Analysis

Scientific paper

A new approach to superstability and finite time extinction of strongly continuous semigroups is presented, unifying known results and providing new criteria for these conditions to hold analogous to the well-known Pazy condition for stability. That finite time extinction implies superstability which is in turn equivalent to several (both known and new) conditions follow from this new approach in a consistent fashion. Examples that the converse statements fail are constructed, in particular, an answer to a question of Balakrishnan on superstable systems not exhibiting finite time extinction.

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