Convex semigroups on $$L^p$$-like spaces

Author:

Denk RobertORCID,Kupper Michael,Nendel Max

Abstract

AbstractIn this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ L p -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ C 0 -semigroup theory extend to the convex case. We prove that the generator of a convex $$C_0$$ C 0 -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 $$C_0$$ C 0 -semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

Mathematics (miscellaneous)

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