The Wave Equation with Memory and Its Controllability

Riccati-based solution to the optimal control of linear evolution equations with finite memory

“…(iii) The absence of (the realization of) a differential operator within the convolution term in (1.1) is a restriction which is rendered milder in view of MacCamy's trick; see e.g. [32,Sections 3.3 and 4.2].…”

“…We point out and give credit to a few pioneering works from the late sixties on, such as [19], [13] and [14]. So, with regard to the broad topic of integro-differential equations the reader is referred to the monographs (listed in cronological order, along with the above-mentioned [35]) by Gripenberg et al [22] (in finite dimensional spaces), Prüss [34] and Pandolfi [32]; [32] is especially valuable for the historical insight and up-to-date references, besides the discussion of modeling and analytical aspects. (In this connection we note that even a higher order PDE such as the Moore-Gibson-Thompson equation 2 has been related -with different aims and in a different fashion -to wave equations with memory; see [15], [4], [5].…”