Large time behavior for the classical wave equation with different regular data and its applications
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915940919148544 |
|---|---|
| author | Chen, Wenhui Ikehata, Ryo |
| author_facet | Chen, Wenhui Ikehata, Ryo |
| contents | In this paper, we mainly consider large time behavior for the classical free wave equation $u_{tt}-Δu=0$ in $\mathbb{R}^n$. We derive some large time optimal estimates for the quantity of solution $\|u(t,\cdot)\|_{L^2}$ with initial data belonging to $L^2$ or with additional weighted $L^1$ integrabilities. Particularly, some thresholds are discovered for the (local or global in time) stabilization of this quantity. We also apply these results to the wave equation with scale-invariant terms, the undamped $σ$-evolution equation, the critical Moore-Gibson-Thompson equation, and the linearized compressible Euler system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large time behavior for the classical wave equation with different regular data and its applications Chen, Wenhui Ikehata, Ryo Analysis of PDEs In this paper, we mainly consider large time behavior for the classical free wave equation $u_{tt}-Δu=0$ in $\mathbb{R}^n$. We derive some large time optimal estimates for the quantity of solution $\|u(t,\cdot)\|_{L^2}$ with initial data belonging to $L^2$ or with additional weighted $L^1$ integrabilities. Particularly, some thresholds are discovered for the (local or global in time) stabilization of this quantity. We also apply these results to the wave equation with scale-invariant terms, the undamped $σ$-evolution equation, the critical Moore-Gibson-Thompson equation, and the linearized compressible Euler system. |
| title | Large time behavior for the classical wave equation with different regular data and its applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.13487 |