A parabolic integro-differential identification problem in a barrelled smooth domain (Q2492117)

The authors consider the problem of recovering a space- and time-dependent kernel in a parabolic integro-differential equation in a barrelled \(C^2\)-domain. They generalize the global existence and uniqueness results of \textit{F. Colombo} and \textit{A. Lorenzi} [J. Math. Anal. Appl. 213, No. 1, 32--62 and 63--90 (1997; Zbl 0892.45006 and Zbl 0892.45007); J. Inverse Ill-posed Probl. 8, No. 5, 505--540 (2000; Zbl 0972.35179)] from cylinders to more general domains, which however are smooth. The \(C^2\)-smoothness enables to use some semigroup properties.