Local well-posedness of generalized BBM equations with generalized damping on 1D torus

Boundary value problems

Junjun Kang¹  Yanbin Tang¹  Yantao Guo² 

[1] School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China;School of Mathematics and Statistics, Xuchang University, Xuchang, P.R. China

关键词: generalized Benjamin-Bona-Mahony equation;    nonlocal operator;    generalized damping;    local well-posedness;    35A07;    35Q53;   

DOI  :  10.1186/s13661-015-0494-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider the periodic initial value problem associated to the generalized Benjamin-Bona-Mahony equation with generalized damping on the one dimensional torus. In contrast to the classical BBM equation, the main difference is that the generalized equation contains two nonlocal operators, and the main difficulty comes from two nonlocal operators. By the fixed point theorem, we prove that the periodic initial value problem is locally well-posed. We also prove that if the solution exists globally in time, it exhibits some asymptotic behavior.

【 授权许可】

CC BY