Abstract

We give new sufficient and practical conditions in terms of the generators ensuring the stability of the critical or the essential type of a perturbed $$C_0$$ -semigroup in general Banach spaces. We apply our theoretical results in order to investigate the control and in particular the time asymptotic behavior of solutions to a broad class of transport equations in $$L^1$$ -spaces and higher dimension. Our results improve, complete and enrich several earlier works.

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