Geodesic
Parabolic Quasi-Variational Inequalities. I: Semimonotone Operator Approach
Journal of convex analysis, Tome 29 (2022) no. 2, pp. 531-558
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Variational inequalities, formulated on unknown-dependent convex sets, are called quasi-variational inequalities (QVI). This paper is concerned with an abstract approach to a class of parabolic QVIs arising in many biochemical/mechanical problems. The approach is based on a compactness theorem for parabolic variational inequalities shown previously by the authors [A new compactness theorem for variational inequalities of parabolic type, Houston J. Math. 44 (2018) 319--350]. The prototype of our model for QVIs of parabolic type is formulated in a reflexive Banach space as the sum of the time-derivative operator under unknown convex constraints and a semimonotone operator, including a feedback system which selects a convex constraint. The main objective of this work is to specify a class of unknown-state dependent convex constraints and to give a precise formulation of QVIs.
Classification : 34G25, 35G45, 35K51, 35K57, 35K59
Mots-clés : Variational inequalities, convex analysis, set-valued monotone operators, parabolic inequalities, superconductivity model 
@article{JCA_2022_29_2_JCA_2022_29_2_a12,
     author = {M. Gokieli and N. Kenmochi and M. Niezg\'odka},
     title = {Parabolic {Quasi-Variational} {Inequalities.} {I:} {Semimonotone} {Operator} {Approach}},
     journal = {Journal of convex analysis},
     pages = {531--558},
     year = {2022},
     volume = {29},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_2_JCA_2022_29_2_a12/}
}
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M. Gokieli; N. Kenmochi; M. Niezgódka. Parabolic Quasi-Variational Inequalities. I: Semimonotone Operator Approach. Journal of convex analysis, Tome 29 (2022) no. 2, pp. 531-558. http://geodesic.mathdoc.fr/item/JCA_2022_29_2_JCA_2022_29_2_a12/