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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 2, 2015

Parabolic variational inequalities with generalized reflecting directions

  • Eduard Rotenstein
From the journal Open Mathematics

Abstract

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.

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Received: 2015-7-17
Accepted: 2015-10-8
Published Online: 2015-12-2

©2015 Eduard Rotenstein

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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