1. Abstract
Consider the initial value problem
where Ω is a bounded domain of ℝn with smooth boundary. In general we are looking for appropiate boundary conditions, such that our problem has a unique solution which depends continuously on the initial data. This time our interest lies on the behaviour of these solutions, i.e., assuming that a first order differential operator A with domain 
generates a strongly continuous semigroup (T(t))t ≥0, we investigate some properties of the corresponding semigroups. These properties are the translation property, the noncompactness property and the relation between the abstract and the concrete Cauchy problem.
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Ulmet, M.G. Properties of Semigroups Generated by First Order Differential Operators. Results. Math. 22, 821–832 (1992). https://doi.org/10.1007/BF03323126
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DOI: https://doi.org/10.1007/BF03323126