Volume 51, Issue 3
Exact Boundary Controllability on a Planar Tree-Like Network of Vibrating Strings with Dynamical Boundary Conditions

Tatsien Li & Yue Wang

J. Math. Study, 51 (2018), pp. 227-252.

Published online: 2018-08

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  • Abstract

This paper concerns a planar tree-like network of vibrating strings with point masses at the nodes. We use a constructive method with modular structure to get the ‘one-sided’ exact boundary controllability for this system with dynamical boundary conditions. Moreover, by constructing the ‘longest’ chain-like subnetwork and its ‘midpoint’, we divide the whole tree-like network into two tree-like sub-networks, and prove the ‘two-sided’exact boundary controllability.

  • Keywords

A planar tree-like network of vibrating strings dynamical boundary condition exact boundary controllability

  • AMS Subject Headings

35L05 35L72 93B05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

dqli@fudan.edu.cn (Tatsien Li)

yue_wang@fudan.edu.cn ( Yue Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-51-227, author = {Li , Tatsien and Wang , Yue }, title = {Exact Boundary Controllability on a Planar Tree-Like Network of Vibrating Strings with Dynamical Boundary Conditions}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {3}, pages = {227--252}, abstract = {

This paper concerns a planar tree-like network of vibrating strings with point masses at the nodes. We use a constructive method with modular structure to get the ‘one-sided’ exact boundary controllability for this system with dynamical boundary conditions. Moreover, by constructing the ‘longest’ chain-like subnetwork and its ‘midpoint’, we divide the whole tree-like network into two tree-like sub-networks, and prove the ‘two-sided’exact boundary controllability.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n3.18.01}, url = {http://global-sci.org/intro/article_detail/jms/12656.html} }
TY - JOUR T1 - Exact Boundary Controllability on a Planar Tree-Like Network of Vibrating Strings with Dynamical Boundary Conditions AU - Li , Tatsien AU - Wang , Yue JO - Journal of Mathematical Study VL - 3 SP - 227 EP - 252 PY - 2018 DA - 2018/08 SN - 51 DO - http://dor.org/10.4208/jms.v51n3.18.01 UR - https://global-sci.org/intro/article_detail/jms/12656.html KW - A planar tree-like network of vibrating strings KW - dynamical boundary condition KW - exact boundary controllability AB -

This paper concerns a planar tree-like network of vibrating strings with point masses at the nodes. We use a constructive method with modular structure to get the ‘one-sided’ exact boundary controllability for this system with dynamical boundary conditions. Moreover, by constructing the ‘longest’ chain-like subnetwork and its ‘midpoint’, we divide the whole tree-like network into two tree-like sub-networks, and prove the ‘two-sided’exact boundary controllability.

Tatsien Li & Yue Wang. (2019). Exact Boundary Controllability on a Planar Tree-Like Network of Vibrating Strings with Dynamical Boundary Conditions. Journal of Mathematical Study. 51 (3). 227-252. doi:10.4208/jms.v51n3.18.01
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