Uniqueness of a pre-generator for C0-semigroup on a general locally convex vector space
نویسندگان
چکیده
The main purpose is to generalize a theorem of Arendt about uniqueness of C0semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for C0semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique L1(Rd, dx) weak solution. This work is partially supported by Yangtze Research Programme, Wuhan University, China, and the Town Council of Hunedoara, Romania. Laboratoire de Mathématiques, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, France, e-mail: [email protected] and Engineering Faculty, ”Politehnica” University, 331128 Hunedoara, Romania. Laboratoire de Mathématiques, CNRS-UMR 6620, Université Blaise Pascal, 63177 Aubière, France. e-mail: [email protected] and Department of Mathematics, Wuhan University, 430072-Hubei, P.R. China. 1
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