Existence and uniqueness of solution for a parabolic equation with p-bilaplacian operator using Rothe's method

In this paper, we investigate a parabolic equation with p-bilaplacian operator, where p > 1. Through an appropriate change of variable, the original problem is transformed into a system of two differential equations. We discretize this system with respect to the time variable, demonstrate the existence and uniqueness of the semi-discrete solution, and prove some a priori estimates.We then use Rothe's method to prove the existence of a unique weak solution to the original problem. Finally, we investigate the order of convergence and prove some error estimates.