WIAS Preprint No. 2446, (2017)

Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints


  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296
  • Strogies, Nikolai

2010 Mathematics Subject Classification

  • 35K86 47J20 49J40 49M15 65J15 65K10


  • Quasi-variational inequality, gradient constraint, dissipative and non-dissipative processes, variable splitting solver




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, respectively. 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.

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