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I do not think such semigroups have been extensively studied. I have seen such semigroups (and, more generally, evolution families corresponding to the non-autonomous problem) in A. Lunardi, M. Geissert, Asymptotic behavior and hypercontractivity in nonautonomous Ornstein-Uhlenbeck equations. J. Lond. Math. Soc. (2) 79 (2009), no. 1, 85--106. |
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I have seen such semigroups (and, more generally, evolution families corresponding to the non-autonomous problem) in A. Lunardi, M. Geissert, Asymptotic behavior and hypercontractivity in nonautonomous Ornstein-Uhlenbeck equations. J. Lond. Math. Soc. (2) 79 (2009), no. 1, 85--106. |
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