The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in higher dimensions
The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in higher dimensions
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DOI：
10.1016/j.matpur.2018.04.009
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Ning-An Lai;Yi Zhou
中科院分区：
文献类型：
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作者：
Ning-An Lai;Yi Zhou
研究了具有Fujita临界指数的半线性阻尼波方程Cauchy问题在小初值条件下经典解的寿命估计。通过使用热核作为检验函数，我们在高维（n≥ 4）中建立了寿命T（ε）≤ exp（C ε− 2 n）的精确上界。然后，与以前的结果一起，在这种情况下，得到了一个完整的结果的尖锐的上下界估计。
This paper is concerned with the lifespan estimate of classical solutions with small initial data to the Cauchy problem of semilinear damped wave equations with the Fujita critical exponent. We establish the following sharp upper bound of the lifespan T (ε)≤ exp(C ε− 2 n) in higher dimensions (n≥ 4), by using the heat kernel as the test function. Then, together with the previous results, a complete result on the sharp lower and upper bound estimates is obtained in this case.