论文标题
分数oscillon方程；与经典Oscillon方程的可溶性和连接
Fractional oscillon equations; solvability and connection with classical oscillon equations
论文作者
论文摘要
在本文中，我们关注的是Oscillon方程非自主分数近似的渐近行为，$$ U_ {tt}-μ（t）ΔU+g+ω（t）u_t = f（t）u_t = f（u），\ x \inΩ $ \ mathbb {r}^n $，$ n \ geqslant 3 $中的平滑域，函数$ω$是时间依赖性的阻尼，$μ$是时间依赖的传播速度，而$ f $是非线性功能。在$ω$和$μ$上的结构假设下，我们从Carvalho，Langa，Robinson，Robinson \ Cite {Clr}和Di Plinio，Duane，Temam，Temam \ Cite \ Cite {ddt1}中建立了分数模型的时间相关吸引子。
In this paper we are concerned with the asymptotic behavior of nonautonomous fractional approximations of oscillon equation $$ u_{tt}-μ(t)Δu+ω(t)u_t=f(u),\ x\inΩ,\ t\in\mathbb{R}, $$ subject to Dirichlet boundary condition on $\partial Ω$, where $Ω$ is a bounded smooth domain in $\mathbb{R}^N$, $N\geqslant 3$, the function $ω$ is a time-dependent damping, $μ$ is a time-dependent squared speed of propagation, and $f$ is a nonlinear functional. Under structural assumptions on $ω$ and $μ$ we establish the existence of time-dependent attractor for the fractional models in the sense of Carvalho, Langa, Robinson \cite{CLR}, and Di Plinio, Duane, Temam \cite{DDT1}.
