论文标题
离散的碎片方程与时间相关系数
Discrete fragmentation equations with time-dependent coefficients
论文作者
论文摘要
我们检查了一个无限的线性系统，该系统是普通微分方程的，该系统模拟了碎片簇的演变，其中每个群集都被假定由相同的单元组成。与以前对此类离散大小碎片模型的研究相反，我们允许随时间变化的片段化系数。通过将系统的初始值问题提出为非自主抽象的库奇问题，在适当加权的$ \ ell^1 $空间中提出，然后利用进化论家族理论的结果，我们证明了物理上相关的，经典的解决方案的存在性和独特性，用于适当约束的系数。
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such discrete-size fragmentation models, we allow the fragmentation coefficients to vary with time. By formulating the initial-value problem for the system as a non-autonomous abstract Cauchy problem, posed in an appropriately weighted $\ell^1$ space, and then applying results from the theory of evolution families, we prove the existence and uniqueness of physically relevant, classical solutions for suitably constrained coefficients.
