无限图上带吸收项的热方程解的熄灭和正性

Extinction and positivity of solutions of the heat equation on infinite graph

摘要: 讨论了无限的、局部有限的、连通图上带吸收项的热方程的非平凡解的大时间行为.利用比较原理和能量方法,证明了其非平凡解在q＜1时熄灭,而在q≥1时保持严格的正性.

Abstract: In this paper,we mainly study the large time behaviors of the nontrivial solutions for the heat equation with the absorption term on the infinite,locally finite,connected graphs.Based on the comparison principle and the energy method,we finally prove that the the solution becomes extinct for q＜1,and remains strictly positive for q≥1.