论文标题
在关键情况下，半连接阻尼波方程的弱耦合系统的急剧寿命估计值
Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
论文作者
论文摘要
在研究较弱的阻尼波动方程或反应扩散方程系统的凯奇问题方面，这个空旷的问题似乎也是最后一部分，迄今为止被称为关键情况下的急剧寿命估计值。在本文中，我们主要研究了关键情况下半连接阻尼波动方程的弱耦合系统的寿命估计。通过使用与非线性差异不平等相关的合适测试功能方法，我们可以在寿命中获取上限估计。此外，我们建立了多项式型类型类型的时间加权空间，以在低空间维度中获得寿命的下限估计。然后，与派生的寿命估计值一起，要求对关键案例中寿命的估计值进行新的和敏锐的结果。最后，在关键情况下，我们将结果应用于半线性反应扩散系统。
The open question, which seems to be also the final part, in terms of studying the Cauchy problem for the weakly coupled system of damped wave equations or reaction-diffusion equations, is so far known as the sharp lifespan estimates in the critical case. In this paper, we mainly investigate lifespan estimates for solutions to the weakly coupled system of semilinear damped wave equations in the critical case. By using a suitable test function method associated with nonlinear differential inequalities, we catch upper bound estimates for the lifespan. Moreover, we establish polynomial-logarithmic type time-weighted Sobolev spaces to obtain lower bound estimates for the lifespan in low spatial dimensions. Then, together with the derived lifespan estimates, new and sharp results on estimates for the lifespan in the critical case are claimed. Finally, we give an application of our results to the semilinear reaction-diffusion system in the critical case.
