Global Existence and Blow-Up for Wave Equations with Weighted Nonlinear Terms in One Space Dimension
Global Existence and Blow-Up for Wave Equations with Weighted Nonlinear Terms in One Space Dimension
复制标题
一维带权非线性项波动方程的全局存在性和放大
DOI：
10.4036/iis.2013.143
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Muhammet Yazici
中科院分区：
文献类型：
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作者：
H. Kubo;A. Osaka;Muhammet Yazici
研究一维非线性加权波动方程的初值问题。在假设初始数据和非线性是奇函数的情况下，我们能够证明小振幅解的全局存在性。我们还证明了在初始数据上的对称假设对于得到全局解是必要的，并给出了一个爆破结果。
We consider the initial value problem for wave equations with weighted nonlinear terms in one space dimension. Under the assumption that the initial data and nonlinearity are odd functions, we are able to show global existence of small amplitude solutions. We also prove that symmetric assumptions on the initial data are necessary to obtain the global solution, by showing a blow-up result.