Nonlinear Parabolic Variational Inequalities with Variable Time-Delay in Time Unbounded Domains

Abstract

We research the well-posedness of the problem without initial condition for nonlinear parabolic variational inequalities with variable time-delay. To justify our results, we impose some assumptions on the solution behavior and growth of the data-in as time variable tends to −∞. Also, we obtain estimates for weak solutions of this problem.

Keywords

• evolution variational inequality
• evolution subdifferential inclusion
• time delay
• fourier problem
• unbounded domain