On continuity in parameters of integrated semigroups

Min He

doi:10.3934/proc.2003.2003.403

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2003, Volume 2003: 403-412. Doi: 10.3934/proc.2003.2003.403 open access

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On continuity in parameters of integrated semigroups

Min He^1,

1.
Department of Mathematical Sciences, Kent State University-Trumbull Campus, Warren, Ohio 44483

Received: August 31, 2002

Revised: February 28, 2003

Published: March 2003

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Abstract

Considering a family of non-densely defined Hille-Yosida operators A($\epsilon$), we discuss continuity in a multi-parameter $\epsilon$ of integrated semigroup S(t, $\epsilon$) generated by A($\epsilon$). Recent developed theorems are given for determining continuity in parameters of integrated semigroup on the entire space. The obtained results are effectively and conveniently employed for some hyperbolic and parabolic types of equations.

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Mathematics Subject Classification: 47D62, 35L20.

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