The Cauchy problem for the nonlinear damped wave equation with slowly decaying data
The Cauchy problem for the nonlinear damped wave equation with slowly decaying data
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DOI：
10.1007/s00030-017-0434-1
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
M. Ikeda;Takahisa Inui;Yuta Wakasugi
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文献类型：
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作者：
M. Ikeda;Takahisa Inui;Yuta Wakasugi
研究了非线性阻尼波动方程的Cauchy问题，在初始值缓慢衰减的情况下，建立了大数据局部适定性和小数据整体适定性。我们还证明了整体解的渐近轮廓由相应抛物问题的解给出，这表明阻尼波动方程的解具有扩散现象.此外，我们还证明了解的爆破，并给出了亚临界非线性方程的寿命估计。特别是，我们确定任何空间维度的临界指数。
We study the Cauchy problem for the nonlinear damped wave equation and establish the large data local well-posedness and small data global well-posedness with slowly decaying initial data. We also prove that the asymptotic profile of the global solution is given by a solution of the corresponding parabolic problem, which shows that the solution of the damped wave equation has the diffusion phenomena. Moreover, we show blow-up of solution and give the estimate of the lifespan for a subcritical nonlinearity. In particular, we determine the critical exponent for any space dimension.