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arXiv · 2508.05955

$L^{2}$-estimates for the linear elastic waves

Hiroshi Takeda
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Abstract

This paper is concerned with the large time behavior of the solution to the Cauchy problem for the elastic wave equations. In particular, optimal $L^{2}$ estimates of the elastic waves are obtained in the sense that the upper and lower bounds of the $L^{2}$ norms of each component of the solution are proved for large $t$, under the minimum assumptions necessary regarding regularity with respect to initial data. The proof is based on the approximation of the solution by a smooth auxiliary function with suitable parameters.

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Hiroshi Takeda. 2025-08-08. $L^{2}$-estimates for the linear elastic waves. https://arxiv.org/abs/2508.05955

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