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Erscheinungsjahr: 
2021
Schriftenreihe/Nr.: 
Center for Mathematical Economics Working Papers No. 712
Verlag: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Zusammenfassung: 
In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having Lp-spaces in mind as a typical application. We show that the basic results from linear C0-semigroup theory extend to the convex case. We prove that the generator of a convex C0-semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup; a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of C0-semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.
Schlagwörter: 
Convex semigroup
nonlinear Cauchy problem
well-posedness and uniqueness
Hamilton-Jacobi-Bellman equation
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