Propagation of singularities for non-linear wave equations in one dimension
Propagation of singularities for non-linear wave equations in one dimension
复制标题
一维非线性波动方程奇点的传播
DOI：
10.1080/0360530780882063
复制
发表时间：
1978
期刊：
影响因子：
--
通讯作者：
M. Reed
中科院分区：
文献类型：
--
作者：
M. Reed
线性波动方程奇异性的传播，即初始数据的奇异性与解的奇异性之间的关系，已经得到了详细的研究并得到了很好的理解;例如，见141、[61]或1121。本文证明了一维非线性波动方程的一个奇性传播定理。结果是，正如预期的那样，奇点沿着光锥的边界传播，但不会传播到内部。这在局部是正确的，如果解决方案是全局的，那么它在全局上也是正确的。证明是完全初等的，并在一定程度上取决于二维波算子的特殊性质。
The propagation of singularities for linear wave equations, that is, the relation between the singularities of the initial data and the singularities of the solution, has received detailed examination and is well understood; see for example 141,[61, or 1121. In this paper we prove a propagation of singularities theorem for non-linear wave equations in one space dimension. The result is that, as expected, singularities propagate along the boundary of the light cone but not into the interior. This is true locally, and if the solution is global, then it is also true globally. The proofs are completely elementary and depend to a certain extent on the special nature of the wave operator in two dimensions.