Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications |
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| Authors: | Dalila Azzam-Laouir Charles Castaing M D P Monteiro Marques |
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| Institution: | 1.Laboratoire de Mathématiques Pures et Appliquées, FSEI,Université Mohammed Seddik Benyahia-Jijel,Jijel,Algeria;2.Département de Mathématiques,Université Montpellier II,Montpellier,France;3.CMAF-CIO, Departamento de Matemática,Faculdade de Ciências da Universidade de Lisboa,Lisboa,Portugal |
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| 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)) → 2 H 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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