000			03455nam a22005415i 4500
001			978-1-4614-5808-1
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008			130220s2013 xxu| s |||| 0|eng d
020			_a9781461458081 _9978-1-4614-5808-1
024	7		_a10.1007/978-1-4614-5808-1 _2doi
050		4	_aQA401-425
072		7	_aPBKJ _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a511.4 _223
100	1		_aErvedoza, Sylvain. _eauthor.
245	1	0	_aNumerical Approximation of Exact Controls for Waves _h[electronic resource] / _cby Sylvain Ervedoza, Enrique Zuazua.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXVII, 122 p. 17 illus., 3 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
505	0		_a1.Numerical approximation of exact controls for waves -- 2.The discrete 1-d wave equation -- 3.Convergence for homogeneous boundary conditions -- 4.Convergence with non-homogeneous data -- 5. Further comments and open problems -- References.
520			_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.
650		0	_aMathematics.
650		0	_aDifferential equations, partial.
650		0	_aSystems theory.
650		0	_aAlgorithms.
650		0	_aNumerical analysis.
650	1	4	_aMathematics.
650	2	4	_aApproximations and Expansions.
650	2	4	_aPartial Differential Equations.
650	2	4	_aSystems Theory, Control.
650	2	4	_aNumerical Analysis.
650	2	4	_aAlgorithms.
650	2	4	_aApplications of Mathematics.
700	1		_aZuazua, Enrique. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461458074
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-5808-1
912			_aZDB-2-SMA
999			_c95507 _d95507