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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1


Volume 13 (2015)

Parabolic variational inequalities with generalized reflecting directions

Eduard Rotenstein
  • Faculty of Mathematics, "Alexandru Ioan Cuza" University of Iaşi, 9 Carol I Blvd., 700506, Iaşi, România
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-12-02 | DOI: https://doi.org/10.1515/math-2015-0083


We study, in a Hilbert framework, some abstract parabolic variational inequalities, governed by reflecting subgradients with multiplicative perturbation, of the following type:

y´(t)+ Ay(t)+0.t Θ(t,y(t)) ∂φ(y(t))∋f(t,y(t)),y(0) = y0,t ∈[0,T]

where A is a linear self-adjoint operator, ∂φ is the subdifferential operator of a proper lower semicontinuous convex function φ defined on a suitable Hilbert space, and Θ is the perturbing term which acts on the set of reflecting directions, destroying the maximal monotony of the multivalued term. We provide the existence of a solution for the above Cauchy problem. Our evolution equation is accompanied by examples which aim to (systems of) PDEs with perturbed reflection.

Keywords: Evolution equations; Oblique reflection; PDEs


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About the article

Received: 2015-07-17

Accepted: 2015-10-08

Published Online: 2015-12-02

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0083.

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©2015 Eduard Rotenstein. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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