...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Computational Physics >On the well-posedness of the stochastic Allen-Cahn equation in two dimensions
【24h】

On the well-posedness of the stochastic Allen-Cahn equation in two dimensions

机译：二维二维随机Allen-Cahn方程的适定性

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical systems in space dimensions d= 1, 2, 3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d≥ 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen-Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that shrinking the mesh size in simulations of the two-dimensional white noise-driven Allen-Cahn equation does not lead to the recovery of a physically meaningful limit.
机译：白噪声驱动的抛物线型非线性随机偏微分方程（SPDE）通常用于对空间维数d = 1、2、3中的物理系统进行建模。对于d≥2，情况是不同的。尽管它们在应用科学中很流行，但通常认为这些SPDE模型的高维版本是数学界所为。我们在由加性白噪声驱动的二维Allen-Cahn方程的特定示例中研究这种差异。由于目前尚不清楚如何定义该方程的弱解的概念，因此我们对噪声进行正则化，并引入一系列近似值。基于启发式的论据和数值实验，我们推测这些近似在连续极限中表现出不同的行为。结果强烈表明，在二维白噪声驱动的Allen-Cahn方程的模拟中缩小网格大小不会导致恢复有意义的物理极限。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号