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In this paper, we consider the following parabolic variational inequality containing a multivalued term and a convex functional: Findu  ∈    L  p   ⁢   (  0  ,  T  ;    W  0   1  ,  p    ⁢   (  Ω  )    ){u\in L^{p}(0,T;W^{1,p}_{0}(\Omega))}    andf  ∈   F  ⁢   (  ⋅  ,  ⋅  ,  u  ){f\in F(\cdot,\cdot,u)}    such thatu  ⁢   (  ⋅  ,  0  )    =   u  0{u(\cdot,0)=u_{0}}    and

On Parabolic Variational Inequalities with Multivalued Terms and Convex Functionals