Existence and Uniqueness of Weak Solutions to the $p$-Biharmonic Parabolic Equation (Communications in Mathematical Research, 2021)
We consider an initial-boundary value problem for a $p$-biharmonic parabolic equation. Under some assumptions on the initial value, we construct approximatesolutions by the discrete-time method. By means of uniform estimates on solutions ofthe time-difference equations, we establish the existence of weak solutions, and alsodiscuss the uniqueness.