Open AccessInput-output $ L^2 $-well-posedness, regularity and Lyapunov stability of string equations on networks
Author(s) -
Dongyi Liu,
Genqi Xu
Publication year - 2022
Publication title -
networks and heterogeneous media
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.732
H-Index - 34
eISSN - 1556-181X
pISSN - 1556-1801
DOI - 10.3934/nhm.2022007
Subject(s) - mathematics , lyapunov function , multiplier (economics) , exponential stability , string (physics) , tree (set theory) , boundary (topology) , function (biology) , pure mathematics , mathematical analysis , mathematical physics , physics , nonlinear system , quantum mechanics , evolutionary biology , biology , economics , macroeconomics
We consider the general networks of elastic strings with Neumann boundary feedbacks and collocated observations in this paper. By selecting an appropriate multiplier, we show that this system is input-output \begin{document}$ L^2 $\end{document} -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.