The obstacle problem for a fourth order semilinear parabolic equation

The obstacle problem for a fourth order semilinear parabolic equation

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...

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Veröffentlicht in:Nonlinear analysis 2020-09, Vol.198, p.111902, Article 111902
Hauptverfasser: Okabe, Shinya, Yoshizawa, Kensuke
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Sprache:eng
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Barriers
Fourth order semilinear parabolic equation
Gradient flow
Minimizing movements
Obstacle problem
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description 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.
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subjects Barriers
Fourth order semilinear parabolic equation
Gradient flow
Minimizing movements
Obstacle problem
title The obstacle problem for a fourth order semilinear parabolic equation
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