Asymptotic Behavior for a Class of Logarithmic Wave Equations with Linear Damping

被引：19

作者：

Hu, Qingying ^{[1
]}

Zhang, Hongwei ^{[1
]}

Liu, Gongwei ^{[1
]}

机构：

[1] Henan Univ Technol, Dept Math, Zhengzhou 450001, Henan, Peoples R China

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2019年 / 79卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Logarithmic wave equation; Initial boundary value problem; Exponential growth; Energy decay; BLOW-UP; GLOBAL EXISTENCE; DECAY; NONEXISTENCE; INSTABILITY;

D O I：

10.1007/s00245-017-9423-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the initial boundary value problem for a class of logarithmic wave equations with linear damping. By constructing apotential well and using the logarithmic Sobolev inequality, we prove that, if the solution lies in the unstable set or the initial energy is negative, the solution will grow as an exponential function in the H01() norm as time goes to infinity. If the solution lies in a smaller set compared with the stable set, we can estimate the decay rate of the energy. These results are extensions of earlier results.

引用

页码：131 / 144

页数：14

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