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Stabilizability of integrodifferential parabolic equations. (English) Zbl 0697.45007
The authors establish a necessary and sufficient condition for the stabilizability of a parabolic integrodifferential equation on an abstract space. This condition reduces to that of Hautus when the kernel of the integral operator is identically zero and the space is finite dimensional. A parabolic integrodifferential equation with a completely monotone kernel and the heat equation for materials with fading memory are also investigated in detail.
Reviewer: C.Constanda

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45M10 Stability theory for integral equations
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