Abstract
This paper considers a class of nonlinear evolution quasi-variational inequality (QVI) problems with pointwise gradient constraints in vector-valued function spaces. The existence and approximation of solutions is addressed based on a combination of $C_0$-semigroup methods, Mosco convergence, and monotone operator techniques developed by Brezis. An algorithm based on semi-discretization in time is proposed and its numerical implementation based on a penalty approach and semismooth Newton methods is studied. This paper ends with a report on numerical tests which involve the $p$-Laplacian and several types of nonlinear constraints.
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