Global existence of solutions for a weakly coupled system of semilinear damped wave equations
Global existence of solutions for a weakly coupled system of semilinear damped wave equations
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DOI：
10.1016/j.jde.2015.05.014
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发表时间：
2015-10
影响因子：
2.4
通讯作者：
K. Nishihara;Yuta Wakasugi
中科院分区：
文献类型：
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作者：
K. Nishihara;Yuta Wakasugi
本文考虑一类弱耦合半线性阻尼波动方程组的柯西问题。我们证明了在超临界的情况下，任何空间维度的小数据的解决方案的整体存在性。我们也给出了估计的加权能量的解决方案，并在一个特殊的情况下，我们证明了一个几乎最优的估计。此外，在亚临界的情况下，我们从上面和下面给出了几乎最优的寿命估计。
In this paper, we consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations. We prove the global existence of solutions for small data in the supercritical case for any space dimension. We also give estimates of the weighted energy of solutions and in a special case, we prove an almost optimal estimate. Moreover, in the subcritical case, we give an almost optimal estimate of the lifespan from both above and below.