Global Asymptotical Behavior of Solutions to a Mixed Pseudo-Parabolic r(x) -Laplacian Equation

被引：0
作者：
Cheng, Jiazhuo [1 ]
Fang, Shaomei [2 ]
Wang, Qiru [1 ,3 ]
机构：
[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China
[2] South China Agr Univ, Coll Math & Informat, Guangzhou 510642, Guangdong, Peoples R China
[3] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China
来源：
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2025年 / 24卷 / 01期
基金：
中国国家自然科学基金;
关键词：
A mixed pseudo-parabolic r(x)-Laplacian; Initial-boundary value problems; Ground state solutions; Asymptotic behavior of global solutions; FINITE-TIME BLOWUP; SCHRODINGER-EQUATION; UP SOLUTIONS; EXISTENCE; NONEXISTENCE; EXTINCTION;
D O I：
10.1007/s12346-024-01195-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concerns the asymptotic behavior of global solutions to the initial-boundary value problem of a mixed pseudo-parabolic r(x)-Laplacian equation. By employing the potential well method and Lagrange multiplier method, we prove the existence of ground state solutions for the stationary problem. Then by applying the Sobolev imbedding inequality and the Holder inequality, we establish a convergence relationship between the global solutions of the evolution problem and the ground state solutions of the corresponding stationary problem.
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页数：18
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