The blow-up curve of solutions to one dimensional nonlinear wave equations with the Dirichlet boundary conditions
The blow-up curve of solutions to one dimensional nonlinear wave equations with the Dirichlet boundary conditions
复制标题
具有狄利克雷边界条件的一维非线性波动方程解的爆炸曲线
DOI：
10.1007/s13160-019-00399-7
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发表时间：
2020
影响因子：
0.9
通讯作者：
Tetsuya Ishiwata and Takiko Sasaki
中科院分区：
文献类型：
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作者：
Tetsuya Ishiwata and Takiko Sasaki
本文考虑半线性波动方程的爆破曲线。Merle和Zaag（Am J Math 134：581-648，2012）考虑了的爆破曲线，并表明存在当初始值改变其符号时爆破曲线在某些点处不可微的情况。他们的分析依赖于问题的变分结构。本文考虑了不具有变分结构的爆破曲线。然而，我们证明了爆破曲线是不可微的，如果初始数据改变其符号，并满足一定的条件。
In this paper, we consider the blow-up curve of semilinear wave equations. Merle and Zaag (Am J Math 134:581–648, 2012) considered the blow-up curve forand showed that there is the case that the blow-up curve is not differentiable at some points when the initial value changes its sign. Their analysis depends on the variational structure of the problem. In this paper, we consider the blow-up curve forwhich does not have the variational structure. Nevertheless, we prove that the blow-up curve is not differentiable if the initial data changes its sign and satisfies some conditions.