具有双稳定型非线性项的Burgers方程的平衡解和行波解分析  

Analysis of stationary solutions and travelling wave solutions for Burgers equation with a bistable nonlinearity

作　　者：丁诗晴 DING Shiqing(School of Applied Mathematics,Nanjing University of Finance and Ecnomics,Nanjing 210023,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《邵阳学院学报（自然科学版）》2023年第2期11-19,共9页Journal of Shaoyang University：Natural Science Edition

摘　　要：为了研究双稳型Burgers方程解的长时间行为,采用相平面分析的方法,得到其平衡解和行波解的完整相图分析。在临界对流情形,证明了存在R上的唯一单调递增平衡解。此外,在所有对流环境下,都会存在groundstate型行波解。方程的两类特殊解可以用来刻画某些流体扩散的稳态情形及前锋的扩张方式。In order to study the long time behavior of the solution of bistable Burgers equation,the phase plane method was used to obtain the complete phase diagram analysis of its stationary solution and traveling wave solutions.In the case of critical convection,it is proved that there is a unique steady solution in R,which increase monotonically.Moreover,groundstate solutions exist in all convection environments.These two kinds of special solutions of the equation can be used to describe the steady state of some fluid diffusion and the expansion mode of the front.

关 键 词：相平面分析 双稳定型非线性项 平衡解 行波解 

分 类 号：O175.26[理学—数学]