for Kindle Fire, Apple, Android, Nook, Kobo, PC, Mac, BlackBerry ...

New to eBooks.com?

Learn more

Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures

Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures by René Dáger
Add to cart
US$ 69.95
(If any tax is payable it will be calculated and shown at checkout.)
This book is devoted to analyze the vibrations of simpli?ed 1? d models of multi-body structures consisting of a ?nite number of ?exible strings d- tributed along planar graphs. We?rstdiscussissueson existence and uniquenessof solutions that can be solved by standard methods (energy arguments, semigroup theory, separation ofvariables,transposition,...).Thenweanalyzehowsolutionspropagatealong the graph as the time evolves, addressing the problem of the observation of waves. Roughly, the question of observability can be formulated as follows: Can we obtain complete information on the vibrations by making measu- ments in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems. UsingtheFourierdevelopmentofsolutionsandtechniquesofNonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total length of the network in a suitable Hilbert space that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree, we characterize these weights in terms of the eigenvalues of the corresponding elliptic problem. The resulting weighted observability inequality allows id- tifying the observable energy in Sobolev terms in some particular cases. That is the case, for instance, when the network is star-shaped and the ratios of the lengths of its strings are algebraic irrational numbers.
Springer Berlin Heidelberg; August 2006
230 pages; ISBN 9783540377269
Read online, or download in secure PDF format
Title: Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures
Author: René Dáger; Enrique Zuazua
 
Buy, download and read Wave Propagation, Observation and Control in 1-d Flexible Multi-Structures (eBook) by René Dáger; Enrique Zuazua today!