论文标题
在具有可变系数的波方程的限制幅度原理上
On the limiting amplitude principle for the wave equation with variable coefficients
论文作者
论文摘要
在本文中，我们证明了有关具有非恒定系数的波方程的限制幅度原理（LAP）的有效性的新结果，不一定以差异形式。在适当的假设对系数和源项上，我们建立了空间维度2和3的膝盖。此结果将其扩展到一个空间维度，并进行适当的修改。我们还量化了膝盖，因此提供了时间域溶液与频域溶液的收敛性估计。我们的证明是基于一些辅助问题解决方案的时间确定结果。在维度1、2和3的径向对称问题上，获得的结果在数值上进行了说明。
In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence form. Under suitable assumptions on the coefficients and on the source term, we establish the LAP for space dimensions 2 and 3. This result is extended to one space dimension with an appropriate modification. We also quantify the LAP and thus provide estimates for the convergence of the time-domain solution to the frequency-domain solution. Our proofs are based on time-decay results of solutions of some auxiliary problems. The obtained results are illustrated numerically on radially symmetric problems in dimensions 1, 2 and 3.
