On the lumpability of linear evolution equations
On the lumpability of linear evolution equations
复制标题
关于线性演化方程的集总性
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
L. Roncoroni
中科院分区：
文献类型：
--
作者：
F. Atay;L. Roncoroni
我们分析了Banach空间上的线性微分方程的集块性，即通过线性约化算子将动态投影到一个更小的状态空间上的可能性，在这个状态空间上存在一个自包含的动态描述。我们首先考虑系统的演化是由有界线性算子描述的，并通过放松一些假设来扩展以前的结果。然后将集块性条件表示为约简算子的核在演化算子下的不变性。其次，作为本文的主要贡献，我们考虑了由无界算子定义的动力学。利用强连续半群理论中的方法，得到了关于约化算子的可集块性条件。我们指出了几个应用程序的特定系统，包括延迟微分方程。
We analyze the lumpability of linear differential equations on Banach spaces, namely, the possibility of projecting the dynamics by a linear reduction operator onto a smaller state space on which a self-contained dynamical description exists. We first consider systems whose evolution is described by bounded linear operators, and extend previous results by relaxing some of the hypotheses. The lumpability condition is then expressed as the invariance of the kernel of the reduction operator under the evolution operator. Next, as the main contribution of the paper, we consider dynamics defined by unbounded operators. We use methods from the theory of strongly continuous semigroups to obtain conditions on the reduction operator for lumpability. We indicate several applications to particular systems, including delay differential equations.