Threshold of singularity formation in the semilinear wave equation
Threshold of singularity formation in the semilinear wave equation
复制标题
半线性波动方程奇点形成阈值
DOI：
10.1103/physrevd.71.044019
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发表时间：
2005
影响因子：
5
通讯作者：
S. Liebling
中科院分区：
文献类型：
--
作者：
S. Liebling
采用分布式自适应网格细化方法，在不假设对称的情况下，对三维半线性波动方程进行数值求解。研究了非线性项指数为$p=5$和$p=7$两种情况下奇点形成的阈值。在奇点形成阈值附近，数值解提出了$p=7$的自相似方法和$p=5$的尺度演化静态解的方法。
Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.