000			02268nam a22003135i 4500
001			65273
005			20210426134530.0
010			_a978-1-4614-5808-1 _dcompra
090			_a65273
100			_a20150401d2013 k||y0pory50 ba
101			_aeng
102			_aUS
200			_aNumerical approximation of exact controls for waves _bDocumento electrónico _fSylvain Ervedoza, Enrique Zuazua
210			_aNew York, NY _cSpringer _d2013
215			_aXVII, 122 p. _cil.
225			_aSpringerBriefs in Mathematics
300			_aColocação: Online
303			_aThis book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these two approaches, which yield similaralgorithms and convergence rates. The discrete approach, however, gives not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability properties of the finite-dimensional approximated dynamics. Moreover, it has the advantage of leading to iterative approximation processes that converge without a limiting threshold in the number of iterations. Such a threshold, which is hard to compute and estimate in practice, is a drawback of the methods emanating from the continuous approach. To complement this theory, the book provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions. The first book to explore these topics in depth, "On the Numerical Approximations of Controls for Waves" has rich applications to data assimilation problems and will be of interest to researchers who deal with wave approximations.
606			_aOndas
606			_aTeoria da aproximação
680			_aQA935
700			_aErvedoza _bSylvain
701			_932352 _4070 _aZuazua _bEnrique
801			_aPT _gRPC
856			_uhttp://dx.doi.org/10.1007/978-1-4614-5808-1
942			_2lcc _cF _n0