ON THE STABILITY AND ASYMPTOTIC BEHAVIOR FOR A QUASI-LINEAR PARABOLIC FLOW

被引：0
|
作者：
Ma, L., I [1 ]
Shi, Z. I. Z. H. E. N. [1 ]
机构：
[1] Univ Sci & Technol Beijing, Sch Math & Phys, Xueyuan Rd 30, Beijing, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Quasi-linear parabolic; global solutions; asymptotic behavior; stability; convergence; FREE-BOUNDARY PROBLEM; CURVATURE FLOW; STATIONARY LINES;
D O I：
10.3934/dcdss.2023053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the stability property and asymptotic be-havior for a quasi-linear parabolic flow in the whole line. We first show the existence and uniqueness of global solutions of the problem. Then we study the stability of the solution to the straight line. We prove the asymptotic behavior or the convergence of the global solution. Similar to the behavior of solutions to heat equation, we prove that the stationary line attracts the graphical curves which surround it.
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页码：620 / 633
页数：14
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