Global existence and asymptotic behavior of solutions for the double dispersive-dissipative wave equation with nonlinear damping and source terms

Boundary value problems

Yadong Shang¹  Huafei Di² 

[1] Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education, Guangzhou, China;School of Mathematics and Information Science, Guangzhou University, Guangzhou, China

关键词: nonlinear wave equation;    double dispersive-dissipative;    global existence;    asymptotic behavior;    damping and source terms;    monotonicity-compactness;    35L35;    35L82;    35B40;   

DOI  :  10.1186/s13661-015-0288-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the initial boundary value problem of the double dispersive-dissipative wave equation with nonlinear damping and source terms. By the combination of the Galerkin method and the monotonicity-compactness method, the existence of global solutions is obtained with the least amount of a priori estimates. Moreover, the asymptotic behavior of global solutions is investigated under some assumptions on the initial data.

【 授权许可】

CC BY