论文标题
用Fujita的关键指数在本地有限的图表上进行半线性热方程式的爆炸
Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs
论文作者
论文摘要
令$ g =（v，e）$为本地有限，连接和加权图。我们证明，对于满足曲率尺寸条件的图形，$ cde'（n，0）$和均匀的多项式体积增长度的度量$ m $，所有非平等的解决方案$ \ partial_tu =Δu=ΔU=ΔU+u^{1+α} $在有限的时间内blowed $ a = \ frac = \ frac} $ {2}。我们还考虑了在某些条件下的爆炸问题，以实现体积增长和初始价值。获得的结果为Lin和Wu在早期论文中的工作提供了显着补充。
Let $G=(V,E)$ be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition $CDE'(n,0)$ and uniform polynomial volume growth of degree $m$, all non-negative solutions of the equation $\partial_tu=Δu+u^{1+α}$ blow up in a finite time provided that $α=\frac{2}{m}$. We also consider the blow-up problem under certain conditions for volume growth and initial value. The obtained results provide a significant complement to the work by Lin and Wu in earlier paper.
