The discrete Morse flow method for parabolic p-Laplacian systems

A regularity for a parabolic p-Laplacian system $$(p>2)$$ is studied by the use of the discrete Morse flow method which is known as one of the ways to approximate a solution to parabolic partial differential equations. Our approximate solution is constructed from the sequence of minimizers of variational functionals whose Euler–Lagrange equations are the time discretized p-Laplacian system. The aim of this paper is to establish that the regularity estimates for the approximate solution hold uniformly on two approximation parameters and show strong convergence of the approximate solution.