论文标题
超临界非线性阻尼的波方程的能量衰减估计
Energy decay estimates for the wave equation with supercritical nonlinear damping
论文作者
论文摘要
我们考虑一个有界域中的阻尼波方程。阻尼是非线性的，并且具有p -1的均匀性，p> 2。首先，我们表明，在超临界情况下，强溶液的能量是t的负能力。只要空间维度不超过十个，衰减率与亚临界或关键情况相同。接下来，依靠新的差异不平等，我们表明，如果进一步需要躺在L P中，则相应的弱解决方案的能量在超临界情况下会衰减。这些新结果补充了文献中的结果，并在超批评阻尼机制的未知土地上打开了重要的违规行为。
We consider a damped wave equation in a bounded domain. The damping is nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that the energy of the strong solution in the supercritical case decays as a negative power of t; the rate of decay is the same as in the subcritical or critical cases, provided that the space dimension does not exceed ten. Next, relying on a new differential inequality, we show that if the initial displacement is further required to lie in L p , then the energy of the corresponding weak solution decays logarithmically in the supercritical case. Those new results complement those in the literature and open an important breach in the unknown land of super-critical damping mechanisms.
