2018/01/29 by Akagi, Goro, Efendiev, Messoud
#35K86 #37B25 #47J35 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1801.09450
This paper is concerned with a fully nonlinear variant of the Allen-Cahn equation with strong irreversibility, where each solution is constrained to be non-decreasing in time. Main purposes of the paper are to prove the well-posedness, smoothing effect and comparison principle, to provide an equivalent reformulation of the equation as a parabolic obstacle problem and to reveal long-time behaviors of solutions. More precisely, by deriving partial energy-dissipation estimates, a global attractor is constructed in a metric setting, and it is also proved that each solution u(x,t) converges to a solution of an elliptic obstacle problem as t → +∞.