论文标题
与空间依赖性阻尼的溶液渐近扩展到波方程
Asymptotic expansion of solutions to the wave equation with space-dependent damping
论文作者
论文摘要
我们研究了在外部结构域中使用空间依赖性阻尼的波动方程解决方案的较大时间行为。我们表明，如果阻尼有效，则该溶液是根据相应抛物线方程的解决方案渐近扩展的。获得渐近膨胀的主要思想是，阻尼波方程的溶液分解为相应的抛物线问题的溶液，以及带有某些不均匀项和初始数据的阻尼波方程溶液的时间衍生物。其余项的估计值是加权方法的应用，并具有相应的抛物线问题的适当超溶液。
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of corresponding parabolic equations. The main idea to obtain the asymptotic expansion is the decomposition of the solution of the damped wave equation into the solution of the corresponding parabolic problem and the time derivative of the solution of the damped wave equation with certain inhomogeneous term and initial data. The estimate of the remainder term is an application of weighted energy method with suitable supersolutions of the corresponding parabolic problem.
