Asymptotic behavior of linear integrodifferential systems
Viorel Barbu and Stanley I. Grossman
Trans. Amer. Math. Soc. 173 (1972), 277-288
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Abstract: We consider the system where is an -vector and and are matrices. System generates a semigroup given by for bounded, continuous and having a finite limit at . Under hypotheses concerning the roots of , where is the Laplace transform, various results about the asymptotic behavior of are derived, generally after invoking the Hille-Yosida theorem. Two typical results are Theorem 1. If and exists for , then for every , there is an such that . Theorem 2. If exists for and if , then the solution to is exponentially asymptotically stable.
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Volterra integrodifferential systems,
exponential asymptotic stability,
solutions in semigroup,
resolvent of semigroup,
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