图上非线性波动方程解的爆破

图作为一种离散结构,可以通过一些有意义的连接来表示离散对象的相互关系,因此,在实际应用中可以将理论模型离散化,是数学、生物学、社会学等领域运用数值模拟解决实际问题的重要工具。图上的偏微分方程可应用于图像分割、动力系统等领域,是人们所关注的热点话题。而图上偏微分方程解的存在性、唯一性和渐近行为等一些性质已经受到众多学者的关注,并得到了大量的研究成果。本文在相关学者研究的基础上用能量方法证明了图上非线性波动方程解的爆破现象,并得出解的爆破时间的上界估计。

As a discrete structure,the graph can represent the interrelationship of discrete objects through some meaningful connections,so the theoretical model can be discretized in practical applications,and it is an important tool for using numerical simulation to solve practical problems in mathematics,biology,sociology and other fields.The partial differential equations on the graph can be applied to image segmentation,dynamical systems and other fields,and are a hot topic of concern.Some properties such as the existence,uniqueness and asymptotic behavior of partial differential equation solutions on graphs have attracted the attention of many scholars and obtained a large number of research results.In this paper,based on the research of relevant scholars,the explosion phenomenon of the solution of the nonlinear wave equation on the graph is proved by energy method,and the upper bound estimate of the burst time of the solution is obtained.