This paper is concerned with the obstacle problem for the L2-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.
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 2020 Sep|
- Fourth order semilinear parabolic equation
- Minimizing movements
- Obstacle problem
ASJC Scopus subject areas
- Applied Mathematics