Coarsening in an integro-differential model of phase transitions
Coarsening in an integro-differential model of phase transitions
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DOI：
10.1017/s0956792500004319
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发表时间：
2000-12-01
影响因子：
1.9
通讯作者：
Stoleriu, I
中科院分区：
文献类型：
--
作者：
Duncan, DB;Grinfeld, M;Stoleriu, I
研究了积分微分方程ε -积分（ω） J(\x - y\)(u(y) - u(x))dy - f(u)， x是ω的一个元素，其中R-n的ω子集J（(.)）大于等于0，ε - > 0和f(u) = u(3) - u（或类似的双稳非线性项），并与Allen-Cahn偏微分方程的结果进行了比较。这两个方程都用作固体相变的模型。特别是，当足够小时，与Allen-Cahn方程的解相比，这个积分-微分方程的解不会变粗。详细探讨了等于1的特殊情况J((.))，从而深入了解了更一般情况下J（(.)）大于或等于0的行为。此外，还概述了一种数值近似方法，并将其用于一维和二维空间的测试，以验证和说明主要结果。
Coarsening of solutions of the integro-differential equation epsilon integral (Omega) J(\x - y\)(u(y) - u(x))dy - f(u), x is an element of Omega,where Omega subset of R-n, J((.)) greater than or equal to 0, epsilon > 0 and f(u) = u(3) - u (or similar bistable nonlinear term), is examined, and compared with results for the Allen-Cahn partial differential equation. Both equations are used as models of solid phase transitions. In particular, it is shown that when epsilon is small enough, solutions of this integro-differential equation do not coarsen, in contrast to those of the Allen-Cahn equation. The special case J((.)) equivalent to 1 is explored in detail, giving insight into the behaviour in the more general case J((.)) greater than or equal to 0. Also, a numerical approximation method is outlined and used on tests in both one- and two-space dimensions to verify and illustrate the main result.