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Convex semigroups on Lp-like spaces

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2021

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http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1hvvqnrwrab710
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https://doi.org/10.1007/s00028-021-00693-3
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Journal of Evolution Equations. Springer. 2021, 21, pp. 2491-2521. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-021-00693-3

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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.

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510 Mathematik

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ISO 690DENK, Robert, Michael KUPPER, Max NENDEL, 2021. Convex semigroups on Lp-like spaces. In: Journal of Evolution Equations. Springer. 2021, 21, pp. 2491-2521. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-021-00693-3
BibTex
@article{Denk2021Conve-53493,
  year={2021},
  doi={10.1007/s00028-021-00693-3},
  title={Convex semigroups on L<sup>p</sup>-like spaces},
  volume={21},
  issn={1424-3199},
  journal={Journal of Evolution Equations},
  pages={2491--2521},
  author={Denk, Robert and Kupper, Michael and Nendel, Max}
}
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