The obstacle problem for a fourth order semilinear parabolic equation. (September 2020) - Okabe, Shinya; Yoshizawa, Kensuke
Abstract: This paper is concerned with the obstacle problem for the L 2 -gradient flow for a functional which is higher order, non-convex and unbounded from below. We prove (i) the existence and uniqueness of local-in-time solutions to the obstacle problem and (ii) a gradient structure of the functional of the solutions, via minimizing movements. Moreover, we show the existence of solutions which blow up in a finite time.