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On the Minimal Extension ofC0-Semigroups for Second-Order Damped Equations

✍ Scribed by Julio R Claeyssen; V Schuchman

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
153 KB
Volume
211
Category
Article
ISSN
0022-247X

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✦ Synopsis

The present paper deals with a minimal extension of the classical semigroup theory for second-order damped differential equations in Banach spaces with closed, densely defined linear operators as coefficients. We do not ask anymore from our operators than in the case of first-order equations, i.e., semigroups. We present here generalizations of the Miyadera᎐Phillips᎐Feller theorem, the Hille type theorem, and the Trotter᎐Kato type theorem. The method is quite general and could be used for equations of any order. We focus our attention on a particular dynamical operator solution or main propagator and we assume some properties about it. From this we can obtain some information about the complementary basis operator solutions or secondary propagators.

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