Abstract
This paper is devoted to the study of evolution problems of the form \(-\frac {du}{dr}(t) \in A(t)u(t) + f(t, u(t))\) in a new setting, where, for each t, A(t) : D(A(t)) → 2H is a maximal monotone operator in a Hilbert space H and the mapping t↦A(t) has continuous bounded or Lipschitz variation on [0, T], in the sense of Vladimirov’s pseudo-distance. The measure dr gives an upper bound of that variation. The perturbation f is separately integrable on [0, T] and separately Lipschitz on H. Several versions and new applications are presented.
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M. D. P. Monteiro Marques was partially supported by Fundação para a Ciência e a Tecnologia, grant UID/MAT/04561/2013.
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Azzam-Laouir, D., Castaing, C. & Monteiro Marques, M.D.P. Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications. Set-Valued Var. Anal 26, 693–728 (2018). https://doi.org/10.1007/s11228-017-0432-9
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DOI: https://doi.org/10.1007/s11228-017-0432-9
Keywords
- Bolza control problem
- Bounded variation
- Lipschitz mapping
- Maximal monotone operators
- Pseudo-distance
- Perturbations
- Skorokhod problem