On the Asymptotic Behavior of Variational Inequalities Set in Cylinders

We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when there is no force term which corresponds to Saint-Venant principle for linear problems. DOI: https://doi.org/10.3934/dcds.2013.33.4875 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-85927 Published Version Originally published at: Chipot, Michel C; Yeressian, Karen (2013). On the asymptotic behavior of variational inequalities set in cylinders. Discrete and Continuous Dynamical Systems Series A, 33(11-12):4875-4890. DOI: https://doi.org/10.3934/dcds.2013.33.4875 DISCRETE AND CONTINUOUS doi:10.3934/dcds.2013.33.4875 DYNAMICAL SYSTEMS Volume 33, Number 11&12, November & December 2013 pp. 4875–4890 ON THE ASYMPTOTIC BEHAVIOR OF VARIATIONAL INEQUALITIES SET IN CYLINDERS Michel Chipot Institute for Mathematics, University of Zurich Winterthurerstrasse 190, CH-8057 Zurich, Switzerland Karen Yeressian Technische Universität Darmstadt, Department of Mathematics Schlossgartenstr. 7, D-64289 Darmstadt, Germany Abstract. We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when there is no force term which corresponds to Saint-Venant principle for linear problems. We study the asymptotic behavior of solutions to variational inequalities with pointwise constraint on the value and gradient of the functions as the domain becomes unbounded. First, as a model problem, we consider the case when the constraint is only on the value of the functions. Then we consider the more general case of constraint also on the gradient. At the end we consider the case when there is no force term which corresponds to Saint-Venant principle for linear problems.