论文标题
解决方案对某些抽象演化方程的稳定性延迟
Stability of solutions to some abstract evolution equations with delay
论文作者
论文摘要
解决方案对延迟微分方程的全局存在和稳定性（*）$ \ dot {u} = a（t）u + g（t，t，u（t-τ）） + f（t）$，$ t \ ge 0 $，$ u（t）= v（t）= v（t）$，$ - $ - $ - $ -CH le t \ le t \ le t \ le 0 $，研究了。这里$ a（t）：\ Mathcal {h} \ to \ Mathcal {h} $是一个封闭的，密集的定义，在Hilbert Space $ \ Mathcal $ \ Mathcal {H} $和$ G（T，U）$中的线性操作员是$ \ MATHCAL {H} $ conting $ c的$ $ to $和$ u的$ \ u $ us t。我们假设$ a（t）$的频谱位于半平面$ \reλ\leγ（t）$中，其中$γ（t）$不一定为负，$ \ | g（t，u）\ | \leα（t）\ | u \ |^p $，$ p> 1 $，$ t \ ge 0 $。在非古典假设下，$ t $倾向于$γ（t）$可以采用正值，提出并证明是合理的，可以使方程式解决方案的解决方案的解决方案，以$ t $的限制并收敛到零。
The global existence and stability of the solution to the delay differential equation (*)$\dot{u} = A(t)u + G(t,u(t-τ)) + f(t)$, $t\ge 0$, $u(t) = v(t)$, $-τ\le t\le 0$, are studied. Here $A(t):\mathcal{H}\to \mathcal{H}$ is a closed, densely defined, linear operator in a Hilbert space $\mathcal{H}$ and $G(t,u)$ is a nonlinear operator in $\mathcal{H}$ continuous with respect to $u$ and $t$. We assume that the spectrum of $A(t)$ lies in the half-plane $\Re λ\le γ(t)$, where $γ(t)$ is not necessarily negative and $\|G(t,u)\| \le α(t)\|u\|^p$, $p>1$, $t\ge 0$. Sufficient conditions for the solution to the equation to exist globally, to be bounded and to converge to zero as $t$ tends to $\infty$, under the non-classical assumption that $γ(t)$ can take positive values, are proposed and justified.
