Science and Education Publishing American Journal of Mathematical Analysis 2333-8431 5 1 2017 3 3 On Weak Solutions of Systems of Strongly Nonlinear Parabolic Variational Inequalities 7 11 EN A.T. El-Dessouky Mathematics Department, Helwan University, Faculty of Science, Cairo, Egypt AJMA2017512 10.12691/ajma-5-1-2 2016 10 5 2017 1 19 2017 3 1 In this paper we prove the existence of weak solutions for systems of variational inequalities of strongly nonlinear parabolic operators: where