@article{Liu2022, 
author = {Dongyi Liu and Genqi Xu},
title = {Input-output        L    2  -well-posedness, regularity and Lyapunov stability of string equations on networks},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {4},
pages = {519-545},
keywords = {Networks of strings, Input-output well-posedness, Regularity, Exponential stability, Multiplier method, Lyapunov functional},
url = {https://www.sciopen.com/article/10.3934/nhm.2022007},
doi = {10.3934/nhm.2022007},
abstract = {We consider the general networks of elastic strings with Neumann boundary feedbacks and collocated observations in this paper. By selecting an appropriate multiplier, we show that this system is input-output        L    2  -well-posed. Moreover, we verify its regularity by calculating the input-output transfer function of system. In the end, by choosing an appropriate multiplier, we give a method to construct a Lyapunov functional and prove the exponential decay of tree-shaped networks with one fixed root under velocity feedbacks acted on all leaf vertices.}
}