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.

翻译：本文证明了变系数波动方程（不必为散度形式）极限振幅原理成立的新结果。在适当的系数与源项假设下，我们建立了二维与三维空间中的极限振幅原理，并通过适当修正将该结果推广至一维空间。此外，我们对极限振幅原理进行定量刻画，从而给出时域解收敛至频域解的估计。本文的证明基于若干辅助问题解的时间衰减结果，并在径向对称问题中通过数值算例展示了所得结论在1、2、3维空间中的有效性。