论文标题
抽象的非线性演化问题：能量衰减
An abstract nonlinear evolution problem: Energy decay
论文作者
论文摘要
在本文中，我们考虑以下非线性进化问题的能量衰减估计$$ \ begin {prippl} [p（u_t（t）] _ t + a u（t） + b（t，x，x，x，u_t（t））= 0，\ quad t \ in J =（0，\ flaty），$ theptions $ nept $ ply $ pus $和$ $ p.发散操作员$ a $。这项工作将Marcati，Nakao，Levin和Pucci在抽象进化方程式上的早期工作扩展到了可能的非线性阻尼。该技术也不同于早期技术。在这里，我们利用修改后的扰动能量技术。
In this paper, we consider energy decay estimates for the following nonlinear evolution problem $$\begin{split} [P(u_t(t))]_t + A u(t) + B(t , x , u_t(t)) =0,\quad t\in J=(0,\infty), \end{split}$$ under suitable assumptions on the self-adjoint operators $P$ and $B$ and the divergence operator $A$. The work extends the earlier work of Marcati, Nakao, Levin and Pucci on abstract evolution equations to the case with possibly nonlinear damping. The technique also differs from earlier techniques. Here, we make use of a modified perturbed energy technique.
