We consider a parabolic Volterra integro-differential equation in Hilbert space with a completely monotone convolution kernel and a sectorial operator. Utilizing a state space setting, we show that for a large class of kernels the state cannot be controlled exactly to zero. On the other hand, equations of our type are always approximately controllable, provided the control operator has dense range
Controllability of a class of Volterra equations in Hilbert spaces with completely monotone kernel
Bonaccorsi, Stefano;
2012
Abstract
We consider a parabolic Volterra integro-differential equation in Hilbert space with a completely monotone convolution kernel and a sectorial operator. Utilizing a state space setting, we show that for a large class of kernels the state cannot be controlled exactly to zero. On the other hand, equations of our type are always approximately controllable, provided the control operator has dense rangeFile in questo prodotto:
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