Sharp higher-order $L^2$-asymptotic expansion of solutions to \sigma-evolution equations with different damping types

Dinh Van Duong; Tuan Anh Dao

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arXiv · 2409.04287

Sharp higher-order $L^2$-asymptotic expansion of solutions to \sigma-evolution equations with different damping types

Dinh Van Duong·Tuan Anh Dao

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Abstract

In this paper, our main goal is to achieve the high-order asymptotic expansion of solutions to $\sigma$-evolution equations with different damping types in the $L^2$ framework. Throughout this, we observe the influence of parabolic like models corresponding to $\sigma_1 \in [0, \sigma/2)$ and $\sigma$-evolution like models corresponding to $\sigma_2 \in (\sigma/2, \sigma]$ on the asymptotic behavior of solutions.

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Dinh Van Duong, Tuan Anh Dao. 2024-09-06. Sharp higher-order $L^2$-asymptotic expansion of solutions to \sigma-evolution equations with different damping types. https://arxiv.org/abs/2409.04287

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