论文标题
一维波方程的指数时间定期，具有有界变化的系数
Exponential time-decay for a one dimensional wave equation with coefficients of bounded variation
论文作者
论文摘要
我们考虑了一个一维波方程的初始值问题，其系数为正，在间隔外且具有界变化（BV）。在对初始数据的紧凑支持的假设下，我们证明了局部能量的时间呈指数速度，并提供了溶液收敛的显式常数。证明的关键要素是对具有BV电位的相关Helmholtz操作员的高频解析估计值。
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges. The key ingredient of the proof is a high frequency resolvent estimate for an associated Helmholtz operator with a BV potential.
