图上带有变指数吸收项的热方程解的熄灭和正性  

Extinction and Positivity of the Solutions to the Heat Equations with Variable Absorption on Graphs

作　　者：辛巧[1] 王坤[1] XIN Qiao WANG Kun(College of Mathematics and Statistics, Yili Normal University, Yining 835000, Chin)

机构地区：[1]伊犁师范学院数学与统计学院,新疆伊宁835000

出　　处：《数学的实践与认识》2017年第18期201-205,共5页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(201442137-30)

摘　　要：通过比较原理,讨论了有限图上带有变指数q(x)>0吸收项的热方程解的熄灭和正性.当q(x)<1时,证明了方程的解在有限时间熄灭,若存在图上的一个内部顶点x_0,有q(x_0)≥1,则方程的解保持严格的正性.By the comparison principal, we mainly study the extinction and positivity of solutions to the heat equation with variable exponent q（x） 〉 0 absorption on finite graph. We prove that the solution becomes extinct in finite time for q（x） 〈 1, on the other hand, if there exists an inner node x0 of the graph such that q（xo） ≥ 1, and then, the solution remains strictly positive.

关 键 词：离散热方程 变指数吸收项 熄灭 图 

分 类 号：O175[理学—数学]