C_0-半群的超稳定性与有限时间灭绝
Superstability and Finite Time Extinction For C_0-Semigroups
摘要：
给出了强连续半群的超稳定性和有限时间绝灭的一种新方法，统一了已有的结果，并提供了新的判据，使这些条件类似于著名的Pazy稳定性条件.有限时间灭绝意味着超稳定性，这反过来又相当于几个（已知的和新的）条件，从这个新的方法在一个一致的方式。例子表明，逆语句失败的构造，特别是，一个问题的答案Balakrishnan超稳定系统不表现出有限时间灭绝。
英文摘要：
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 showing 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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