Existence and uniqueness for solutions of parabolic quasi-variational inequalities with impulse control and nonlinear source terms

In this paper, we present a new proof for the existence and uniqueness of solutions of parabolic quasivariational inequalities with impulse control. We prove some properties of the presented algorithm (see [S. Boulaaras, M. Haiour, Appl. Math. Comput., 217 (2011), 6443-6450], [S. Boulaaras, M. Haiour, Indaga. Math., 24 (2013), 161-173]) using a semi-implicit scheme with respect to the t-variable combined with a finite element spatial approximation.