## Uniqueness of $$C _{0}$$-semigroups on a general locally convex vector space and an application.(English)Zbl 1227.47026

In this paper, the authors generalize a well known result due to W. Arendt [in: R. Nagel (ed.), “One-parameter semigroups of positive operators”, Lecture Notes in Mathematics 1184. Berlin etc.: Springer-Verlag (1986; Zbl 0585.47030), doi:10.1007/BFb0074924, Theorem 1.33, p. 46]. Their result concerns the uniqueness of $$C_0$$-semigroups in the setting of general locally convex vector spaces. More precisely, they prove that the cores are the only domains of uniqueness for $$C_0$$-semigroups on locally convex spaces. They apply their result to the mass transport equation and they find a necessary and sufficient condition for the uniqueness of an $$L^1$$ weak solution of such an equation.

### MSC:

 47D06 One-parameter semigroups and linear evolution equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34G10 Linear differential equations in abstract spaces

Zbl 0585.47030
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### References:

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