图上带指数源项ω-扩散方程解的爆破现象  

Blowup phenomenon of solutions of ω-diffusion equation with exponential source term on the graph

作　　者：周亚新 黄琳 朱立平[1] ZHOU Yaxin;HUANG Lin;ZHU Liping(School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《纺织高校基础科学学报》2022年第2期92-97,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11702206)。

摘　　要：讨论在图上Dirichlet边界条件下带有指数项方程解的爆破现象。通过巴拿赫不动点定理证明解的存在唯一性,用上下解的方法证明了解在有限时间内爆破,并对方程中的f(t,α)分为e^(αt)和t^(α)等2种情况讨论,分别给出爆破时间和爆破率的估计。在3个不同的图上用数值模拟说明解的爆破行为,发现在相同的条件下,e^(αt)比t^(α)的爆破时间更短。The blowup phenomenon of the solution of the equation with exponential terms under the Dirichlet boundary condition on the graph is discussed.The existence and uniqueness of the solution is proved by Banach’s fixed point theorem,the blow up of the solution in finite time is proved by the method of upper and lower solutions.Then f(t,α)in the equation can be e^(αt)and t^(α),the estimates of blowup time and blowup rate are given respectively.The blowup behavior of the solution is illustrated by numerical simulation on three different graphs.It is found that under the same conditions,the blowup time of e^(αt)is shorter than that of t^(α).

关 键 词：简单图 指数项 爆破时间 爆破率 差分法 

分 类 号：O175.2[理学—数学]