Stabilizability of integrodifferential parabolic equations. (English) Zbl 0697.45007

Da Prato, Giuseppe; Lunardi, Alessandra

J. Integral Equations Appl. 2, No. 2, 281-304 (1990).

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

MSC:

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

Keywords:

stabilizability; parabolic integrodifferential equation; abstract space; completely monotone kernel; heat equation for materials with fading memory