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math.AP2021
Construction of excited multi-solitons for the focusing 4D cubic wave equation
Xu Yuan
Consider the focusing 4D cubic wave equation \[ \partial_{tt}u-Δu-u^{3}=0,\quad \mbox{on}\ (t,x)\in [0,\infty)\times \mathbb{R}^{4}.\] The main result states the existence in energ…
math.AP2021
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
Raphaël Côte, Xu Yuan
We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with , $2 \le N…