Abstract: We gave the existence of the optimal control function for the initial  boundary value problem of evolution p-Laplace equations by taking the limit of the minimizing sequences of the cost functional. Firstly, we studied the existence and uniqueness of the solution to the problem by using the energy estimate method. Secondly,  we analyzed convergence of the minimizing sequences of the cost functional by using compact estimates and compact imbedding theorem. Finally, we proved  the existence of the the optimal control function.

Key words: evolution p-Laplace equation, optimal control, boundary control