An Optimal Estimate for the Time Singular Limit of an Abstract Wave Equation
An Optimal Estimate for the Time Singular Limit of an Abstract Wave Equation
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抽象波动方程时间奇异极限的最优估计
DOI：
10.1619/fesi.47.277
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
A. Haraux
中科院分区：
文献类型：
--
作者：
R. Chill;A. Haraux
R.池田最近证明了一些积分估计之间的差异的解决方案的抽象热方程和解决方案的抽象波动方程的结果从热方程的时间奇异摄动。如果适当地选择初始值，则获得估计。我们证明了一个逐点估计，它改善了上述结果的大倍到几个方向，我们还建立了这个估计的最优性的波动方程的外部区域。我们的证明依赖于无界自伴算子的谱定理。
R. Ikehata recently proved some integral estimate for the difference between the solution of an abstract heat equation and the solution of an abstract wave equation which results from the heat equation by a time singular perturbation. The estimate is obtained if the initial values are chosen appropriately. We prove a pointwise estimate which improves the above result for large times into several directions, and we also establish the optimality of this estimate for the wave equation in an exterior domain. Our proofs rely on the spectral theorem for unbounded self-adjoint operators.