数学杂志2026，Vol.46Issue(3)：125-133,9.
图上无界拉普拉斯算子非线性抛物方程解的存在性和爆破现象
THE EXISTENCE OF SOLUTIONS AND BLOW-UP PHENOMENON TO THE PARABOLIC EQUATION FOR UNBOUNDED LAPLACIANS ON THE GRAPHS
朱立平 1黄大伟1
作者信息
- 1. 西安建筑科技大学理学院,陕西西安 710055
- 折叠
摘要
Abstract
In this paper,we study the existence and blow-up of solutions to a nonlinear parabolic equation with unbounded Laplace operators on locally finite graphs:ut=Δu+h(x)f(u(x,t)).First,the existence and uniqueness of mild solutions in a short time interval are established using the Banach fixed-point theorem.Then,by skillfully constructing auxiliary functions and under appropriate conditions concerning polynomial growth of the graph and the nonlinearity f,the finite-time blow-up of mild solutions is proved via heat kernel estimates.These results extend those in the literature[13].关键词
无界拉普拉斯算子/爆破/抛物方程Key words
unbounded Laplacians operator/blow-up/parabolic equation分类
数理科学引用本文复制引用
朱立平,黄大伟..图上无界拉普拉斯算子非线性抛物方程解的存在性和爆破现象[J].数学杂志,2026,46(3):125-133,9.
