



























Abstract:We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial radial stationary solution $W$, called the ground state, which is unique up to sign and scale. We prove that any bounded energy norm solution behaves asymptotically as a superposition of the modulated ground states and a radiation term. In the global case, particularly, the solution converges to a pure multi-bubble due to the damping effect.
From: Jingyuan Gu [view email]
[v1]
Fri, 22 Dec 2023 07:41:13 UTC (55 KB)
[v2]
Tue, 12 Mar 2024 02:02:14 UTC (58 KB)
[v3]
Tue, 23 Jun 2026 04:03:00 UTC (88 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。