Sharp lifespan estimates and blow-up rates for the semilinear wave equation with time-dependent damping and subcritical nonlinearities

Sharp lifespan estimates and blow-up rates for the semilinear wave equation with time-dependent damping and subcritical nonlinearities
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发表时间：
2016-09
期刊：
arXiv: Analysis of PDEs
影响因子：
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通讯作者：
K. Fujiwara;M. Ikeda;Yuta Wakasugi
K. Fujiwara;M. Ikeda;Yuta Wakasugi
中科院分区：
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文献类型：
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作者：
K. Fujiwara;M. Ikeda;Yuta Wakasugi

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我们研究具有瞬态阻尼的半线性波动方程柯西问题解的爆炸行为。当阻尼有效且非线性为亚临界时，我们显示了解决方案的爆炸率和急剧的寿命估计。较高的估计值由 ODE 论证证明，较低的估计值由缩放变量的方法给出。
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.