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- Title
Stabilization of one-dimensional wave equations coupled with an ODE system on general tree-shaped networks.
- Authors
DONGYI LIU; LIPING ZHANG; GENQI XU; ZHONGJIE HAN
- Abstract
By the theory of Sturm-Liouville eigenvalue problems, it is shown that the stability of one-dimensional wave equations with variable coefficients coupled with an ordinary differential equation (ODE) system on general tree-shaped networks is equivalent to that of its subsystem (called the base system). Thus, it is proved that the coupled system can arrive at asymptotical stability, if, for every interior vertex of the subsystem, the spectra of any two edges joined one common interior vertex of the subsystem are disjoint. Especially, the coupled system with one fixed root is exponentially stable. In the end, a star with three edges and a tree-shaped networks with 10 edges are given to verify the theoretical results.
- Subjects
NUMERICAL solutions to Sturm-Liouville equations; NONLINEAR wave equations; ORDINARY differential equations; COUPLED problems (Complex systems) -- Numerical solutions; EXPONENTIAL stability
- Publication
IMA Journal of Mathematical Control & Information, 2015, Vol 32, Issue 3, p557
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnu008