L2$L^{2}$‐growth property for the wave equation with a higher derivative term.
Published In: Mathematische Nachrichten, 2024, v. 297, n. 10. P. 3625 1 of 3
Database: Academic Search Ultimate 2 of 3
Authored By: Li, Xiaoyan; Ikehata, Ryo 3 of 3
Abstract
We consider the Cauchy problem in Rn${\bf R}^{n}$ for the wave equation with a higher derivative term. We derive sharp growth estimates of the L2$L^{2}$‐norm of the solution itself for the case of n=1$n = 1$ and n=2$n = 2$. By imposing the weighted L1$L^{1}$‐initial velocity, we can get the lower and upper bound estimates of the solution itself. For the case of n≥3$n\ge 3$, we observe that the L2$L^{2}$‐growth behavior of the solution never occurs in the (L2∩L1)$(L^{2}\cap L^{1})$‐framework of the initial data. [ABSTRACT FROM AUTHOR]
Additional Information
- Source:Mathematische Nachrichten. 2024/10, Vol. 297, Issue 10, p3625
- Document Type:Article
- Subject Area:Physics
- Publication Date:2024
- ISSN:0025-584X
- DOI:10.1002/mana.202300358
- Accession Number:180217284
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