Blow-up theorem for semilinear wave equations with non-zeroinitial position
Blow-up theorem for semilinear wave equations with non-zeroinitial position
复制标题
非零初始位置半线性波动方程的爆炸定理
DOI：
10.1016/j.jde.2010.01.010
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Kyouhei Wakasa
中科院分区：
文献类型：
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作者：
Hiroyuki Takamura;Hiroshi Uesaka;Kyouhei Wakasa
半线性波动方程解的特征之一可以在非紧支撑数据的爆破结果中找到。尽管有限的线性波的传播速度，我们没有任何权力的非线性，如果初始数据的空间衰减是弱的时间的整体解决方案。这是由Asakura（1986）[2]首先观察到的，发现了一个临界衰减以确保解的整体存在性。但爆破结果只适用于零初始位置具有正速度的情况。本文将Uesaka（2009）[22]关于非零初始位置的Blow-up定理推广到高维情形。并放宽了对非线性项的假设，以包括一个例子，|u| p−1u。此外，通过实例阐明了初始位置的临界衰减。
One of the features of solutions of semilinear wave equations can be found in blow-up results for non-compactly supported data. In spite of finite propagation speed of the linear wave, we have no global in time solution for any power nonlinearity if the spatial decay of the initial data is weak. This was first observed by Asakura (1986) [2] finding out a critical decay to ensure the global existence of the solution. But the blow-up result is available only for zero initial position having positive speed. In this paper the blow-up theorem for non-zero initial position by Uesaka (2009) [22] is extended to higher-dimensional case. And the assumption on the nonlinear term is relaxed to include an example, |u|p−1u. Moreover the critical decay of the initial position is clarified by example.