论文标题
具有一般非线性的强阻尼波方程的初始边界值问题
Initial boundary value problem for a strongly damped wave equation with a general nonlinearity
论文作者
论文摘要
在本文中，考虑了具有一般非线性的强阻尼半线性波方程。借助新构建的辅助功能和凹陷论证，为此问题建立了一般有限的时间爆破标准。此外，弱解的寿命是从上方和下方估算的。这部分扩展了最近的文献中获得的一些结果，并阐明了功率类型的非线性和对数非线性对解决这些问题的有限时间爆炸的相似效果。
In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated from both above and below. This partially extends some results obtained in recent literatures and sheds some light on the similar effect of power type nonlinearity and logarithmic nonlinearity on finite time blow-up of solutions to such problems.
