TY - JOUR
T1 - The obstacle problem for a fourth order semilinear parabolic equation
AU - Okabe, Shinya
AU - Yoshizawa, Kensuke
N1 - Funding Information:
The first author was partially supported by JSPS KAKENHI Grant Nos. 19H05599 and 16H03946 . The second author was supported by the JSPS, Japan KAKENHI Grant No. 19J20749 .
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/9
Y1 - 2020/9
N2 - 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.
AB - 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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U2 - 10.1016/j.na.2020.111902
DO - 10.1016/j.na.2020.111902
M3 - Article
AN - SCOPUS:85083302051
VL - 198
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
M1 - 111902
ER -