Hyperbolic-like estimates for higher order equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

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: Hyperbolic higher order equations;    Energy estimates;    Dissipative effects;   

DOI  :  10.1016/j.jmaa.2012.05.070

来源: Elsevier

【 摘 要 】

The main goal of this paper is to derive long time estimates of the energy for the higher order hyperbolic equations with time-dependent coefficients. in particular, we estimate the energy in the hyperbolic zone of the extended phase space by means of a function f (t) which depends on the principal part and on the coefficients of the terms of order m - 1. Then we look for sufficient conditions that guarantee the same energy estimate from above in all the extended phase space. We call this class of estimates hyperbolic-like since the energy behavior is deeply depending on the hyperbolic structure of the equation. In some cases, these estimates produce a dissipative effect on the energy. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free