On Systems of Parabolic Variational Inequalities with Multivalued Terms
In this paper we present an analytical framework for the following system of multivalued parabolic variational inequalities in a cylindrical domain [Formula] where Kk is a closed and convex subset of [Formula], Ak is a time-dependent quasilinear elliptic operator, and fk: Q x ℝm → 2ℝ is an upper semicontinuous multivalued function with respect to s ∈ ℝm. We provide an existence theory for the above system under certain coercivity assumptions. In the noncoercive case, we establish an appropriate sub-supersolution method that allows us to get existence and enclosure results. As an application, a multivalued parabolic obstacle system is treated. Moreover, under a lattice condition on the constraints Kk, systems of evolutionary variational-hemivariational inequalities are shown to be a subclass of the above system of multivalued parabolic variational inequalities.
S. Carl and V. K. Le, "On Systems of Parabolic Variational Inequalities with Multivalued Terms," Monatshefte fur Mathematik, vol. 194, no. 2, pp. 227-260, Springer, Feb 2021.
The definitive version is available at https://doi.org/10.1007/s00605-020-01477-6
Mathematics and Statistics
Keywords and Phrases
Evolutionary variational-hemivariational inequalities; Multivalued parabolic variational inequality; Obstacle problem; Pseudomonotone multivalued operator; Sub-supersolution; System of parabolic variational inequalities; Upper semicontinuous multivalued operator
International Standard Serial Number (ISSN)
Article - Journal
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01 Feb 2021