Allen-Cahn equation with strong irreversibility
Allen-Cahn equation with strong irreversibility
复制标题
具有强不可逆性的 Allen-Cahn 方程
DOI：
10.1017/s0956792518000384
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发表时间：
2019
影响因子：
1.9
通讯作者：
Goro Akagi and Messoud Efendiev
中科院分区：
文献类型：
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作者：
Goro Akagi and Messoud Efendiev
本文研究了具有强不可逆性的Allen-Cahn方程的一个完全非线性变形，其中每个解都被约束为在时间上是非减的。本文的主要目的是证明适定性、光滑效应和比较原理，提供一个等价的抛物障碍问题的方程，并揭示长时间的行为的解决方案。更精确地说，通过导出部分能量耗散估计，构造了度量环境下的整体吸引子，并证明了当t → +∞时，每个解u（x，t）收敛于椭圆障碍问题的解.
This paper is concerned with a fully non-linear variant of the Allen–Cahn equation with strong irreversibility, where each solution is constrained to be non-decreasing in time. The main purposes of this 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 behaviours 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 → +∞.