Convex semigroups on Lp -like spaces

Denk R, Kupper M, Nendel M (2021)
Journal of Evolution Equations.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Denk, Robert; Kupper, Michael; Nendel, MaxUniBi
Abstract / Bemerkung
In this paper, we investigate convex semigroups on Banach lattices with order continuous norm. having L-p-spaces in mind as a typical application. We show that the basic results from linear C-0-semigroup theory extend to the convex case. We prove that the generator of a convex 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-semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.
Stichworte
Convex semigroup; Nonlinear Cauchy problem; Well-posedness and; uniqueness; Hamilton-Jacobi-Bellman equation
Erscheinungsjahr
2021
Zeitschriftentitel
Journal of Evolution Equations
ISSN
1424-3199
eISSN
1424-3202
Page URI
https://pub.uni-bielefeld.de/record/2954681

Zitieren

Denk R, Kupper M, Nendel M. Convex semigroups on Lp -like spaces. Journal of Evolution Equations. 2021.
Denk, R., Kupper, M., & Nendel, M. (2021). Convex semigroups on Lp -like spaces. Journal of Evolution Equations. https://doi.org/10.1007/s00028-021-00693-3
Denk, R., Kupper, M., and Nendel, M. (2021). Convex semigroups on Lp -like spaces. Journal of Evolution Equations.
Denk, R., Kupper, M., & Nendel, M., 2021. Convex semigroups on Lp -like spaces. Journal of Evolution Equations.
R. Denk, M. Kupper, and M. Nendel, “Convex semigroups on Lp -like spaces”, Journal of Evolution Equations, 2021.
Denk, R., Kupper, M., Nendel, M.: Convex semigroups on Lp -like spaces. Journal of Evolution Equations. (2021).
Denk, Robert, Kupper, Michael, and Nendel, Max. “Convex semigroups on Lp -like spaces”. Journal of Evolution Equations (2021).

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