  In this paper, we present a numerical verification method of solutions for
nonlinear parabolic initial boundary value problems. Decomposing the problem
into a nonlinear part and an initial value part, we apply Nakao's projection
method, which is based on the full-discrete finite element method with
constructive error estimates, to the nonlinear part and use the theoretical
analysis for the heat equation to the initial value part, respectively. We show
some verified examples for solutions of nonlinear problems from initial value
to the neighborhood of the stationary solutions, which confirm us the actual
effectiveness of our method.
