000			04672nam a22004815i 4500
001			978-0-387-23218-8
003			DE-He213
005			20250710083927.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387232188 _a99780387232188
024	7		_a10.1007/b100958 _2doi
082	0	4	_a519 _223
100	1		_aRamm, Alexander G. _eauthor.
245	1	0	_aInverse Problems _h[recurso electrónico] : _bMathematical and Analytical Techniques with Applications to Engineering / _cby Alexander G. Ramm.
264		1	_aBoston, MA : _bSpringer US, _c2005.
300			_aXX, 442 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aMethods of Solving Ill-Posed Problems -- One-Dimensional Inverse Scattering and Spectral Problems -- Inverse Obstacle Scattering -- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data -- Non-Uniqueness and Uniqueness Results -- Inverse Problems of Potential Theory and Other Inverse Source Problems -- Non-Overdetermined Inverse Problems -- Low-Frequency Inversion -- Wave Scattering by Small Bodies of Arbitrary Shapes -- The Pompeiu Problem.
520			_aInverse problems are the problems that consist of finding an unknown property of an object or a medium from the observation or a response of this object or a medium to a probing signal. Thus the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.) objects immersed in water (submarines, fish) and in many other situations. This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter. New results include recovery of a potential from I-function and applications to classical and new inverse scattering and spectral problems, study of inverse problems with"incomplete data", study of some new inverse problems for parabolic and hyperbolic equations, discussion of some non-overdetermined inverse problems, a study of inverse problems arising in the theory of ground-penetrating radars, development of DSM (dynamical systems method) for solving ill-posed nonlinear operator equations, comparison of the Ramm's inversion method for solving fixed-energy inverse scattering problem with the method based on the Dirichlet-to-Neumann map, derivation of the range of applicability and error estimates for Born's inversion, a study of some integral geometry problems, including tomography, inversion formulas for the spherical means, proof of the invertibility of the steps in the Gel'fand-Levitan and Marchenko inversion procedures, derivation of the inversion formulas and stability estimates for the multidimensional inverse scattering problems with fixed-energy noisy discrete data, new uniqueness and stability results in obstacle inverse scattering, formulation and a solution of an inverse problem of radiomeasurements, methods for finding small inhomogeneities from surface scattering data.
650		0	_aENGINEERING.
650		0	_aCOMPUTER VISION.
650		0	_aDIFFERENTIAL EQUATIONS.
650		0	_aMATHEMATICS.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aENGINEERING MATHEMATICS.
650	1	4	_aENGINEERING.
650	2	4	_aAPPL.MATHEMATICS/COMPUTATIONAL METHODS OF ENGINEERING.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aMATHEMATICAL AND COMPUTATIONAL PHYSICS.
650	2	4	_aIMAGE PROCESSING AND COMPUTER VISION.
650	2	4	_aORDINARY DIFFERENTIAL EQUATIONS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387231952
856	4	0	_uhttp://dx.doi.org/10.1007/b100958 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-ENG
942			_2ddc _cER
999			_c56156 _d56156