论文标题
一维阻尼非线性klein-gordon方程的长期渐近学
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation
论文作者
论文摘要
对于一维非线性抑制klein-gordon方程\ [\ partial_ {t}^{2} u+2α\ partial_ {t} t} $ \ mathbb {r} \ times \ times \ mathbb {r} $，} \]带有$α> 0 $和$ p> 2 $，我们证明，任何全球有限能量解决方案要么会收敛到$ 0 $，要么以$ t \ y y y y y to $ t \ to $ t \ to \ iffty $ histty $作为$ k \ egeq geq 1 $ $ $ $ $ decoupled solepled decoupled decoupled decoupled decoupled decoupled wave。在Multi-Soliton Case $ K \ geq 2 $中，单个波浪有其他标志，其距离为订单$ \ log t $。
For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2α\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on $\mathbb{R}\times\mathbb{R}$,}\] with $α>0$ and $p>2$, we prove that any global finite energy solution either converges to $0$ or behaves asymptotically as $t\to \infty$ as the sum of $K\geq 1$ decoupled solitary waves. In the multi-soliton case $K\geq 2$, the solitary waves have alternate signs and their distances are of order $\log t$.
