Stability Conditions for Abstract Functional Differential Equations in Hilbert Space |
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Authors: | Mastinek |
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Institution: | (1) EPF-University of Maribor Razlagova 14 2000 Maribor, Slovenia mastinsek@uni-mb.si, SI |
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Abstract: | Abstract. Stability conditions for functional differential equations of the form: du (t)/ dt = Au(t)+ bAu(t-h)+(a^\ast Au)(t) are studied, where A is the infinitesimal generator of an analytic semigroup in a Hilbert space, b\neq 0 and the convolution term contains a square integrable real function a\neq 0 . Norm discontinuity of the solution semigroup of the equation with discrete delay is avoided by studying the inverse of
the characteristic operator. Sufficient and necessary conditions for the uniform exponential stability of the solution semigroup
are obtained. The results are applied to a retarded partial integrodifferential equation. |
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Keywords: | |
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