Eigenvalue asymptotics for the damped wave equation on metric graphs

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Freitas, Pedro^1,2  Lipovsky, Jiri³ 

[1] Univ Lisbon, Fac Human Kinet, Dept Math, Lisbon, Portugal

[2] Univ Lisbon, Fac Sci, Grp Math Phys, Edificio C6, P-1749016 Lisbon, Portugal

[3] Univ Hradec Kralove, Fac Sci, Dept Phys, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic

关键词: Damped wave equation;    Metric graphs;    Spectrum;   

DOI  :  10.1016/j.jde.2017.04.012

来源: Elsevier

【 摘 要 】

We consider the linear damped wave equation on finite metric graphs and analyse its spectral properties with an emphasis on the asymptotic behaviour of eigenvalues. In the case of equilateral graphs and standard coupling conditions we show that there is only a finite number of high-frequency abscissas, whose location is solely determined by the averages of the damping terms on each edge. We further describe some of the possible behaviour when the edge lengths are no longer necessarily equal but remain commensurate. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free