论文标题
非径向解决方案的外部散射到能量亚临界波动方程
Exterior scattering of non-radial solutions to energy subcritical wave equations
论文作者
论文摘要
我们考虑了defocusing，doctial_t^2 u-ΔU= - | | | |^{p -1} u $ in dimension $ d \ in \ in \ {3,4,5 \} $，并证明解决方案的外部散布$ 3 \ leq d \ leq d \ leq 5 $和$ 1+6/d <p <p p <，更确切地说，如果有有限能量的任何解决方案，则存在解决方案$ u_l $对均匀的线性波方程，以便以下限制成立 \ [ \ lim_ {t \ rightarrow +\ infty} \ int_ {| x |> t +t +t +t +r} | \ nabla_ {x，x，t} u（x，x，x，t） - \ nabla_ {x，x，t} u_l（x，t} u_l（x，x，x，x，x，x，x，x，x，t）|^2 dx = 0 \ \ \] 对于任何固定的实际数字$ r $。在径向情况下，这概括了先前已知的外部散射。
We consider the defocusing, energy subcritical wave equation $\partial_t^2 u - Δu = -|u|^{p-1} u$ in dimension $d \in \{3,4,5\}$ and prove the exterior scattering of solutions if $3\leq d \leq 5$ and $1+6/d<p<1+4/(d-2)$. More precisely, given any solution with a finite energy, there exists a solution $u_L$ to the homogeneous linear wave equation, so that the following limit holds \[ \lim_{t\rightarrow +\infty} \int_{|x|>t+R} |\nabla_{x,t} u(x,t)- \nabla_{x,t} u_L(x,t)|^2 dx = 0 \] for any fixed real number $R$. This generalize the previously known exterior scattering result in the radial case.
