Dissipative and Non-Dissipative Evolutionary Quasi-Variational Inequalities with Gradient Constraints

  • M. Hintermüller
  • C. N. Rautenberg
  • N. Strogies


Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.


Quasi-variational inequality Gradient constraint Dissipative and non-dissipative processes Variable splitting solver 

Mathematics Subject Classification (2010)

35K86 47J20 49J40 49M15 65J15 65K10 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Department of MathematicsHumboldt-University of BerlinBerlinGermany

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