A class of dissipative wave equations with time-dependent speed and damping

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:399

Article

D'Abbicco, M.¹  Ebert, M. R.² 

[1] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy

[2] Univ Sao Paulo, FFCLRP, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP, Brazil

关键词: Damped wave equation;    Variable speed of propagation;    Energy estimates;    Dissipative effects;   

DOI  :  10.1016/j.jmaa.2012.10.017

来源: Elsevier

【 摘 要 】

We study the long time behavior of the energy for wave-type equations with time-dependent speed and damping: u(tt) - lambda(t)(2) Delta u + b(t)u(t) = 0. We investigate the interaction between the speed of propagation lambda(t) and the damping coefficient b(t), showing how to describe the dissipative effect on the energy. We study a class of dissipations for which the equation keeps its hyperbolic structure and properties. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free