000			03821nam a2200409 i 4500
008			090928s2010 riua b 001 0 eng
010			_a2009037756
020			_a9780821849040 _qalk. paper
020			_a0821849042 _qalk. paper
035			_a.b6838953x
040			_aDLC _beng _cDLC _dYDX _dYDXCP _dUBY _dIXA _dOSU _dUtOrBLW _dBAUN _erda
041	1		_aeng _hger
049			_aBAUN_MERKEZ
050	0	4	_aQA402.3 _b.T7913 2010
082	0	0	_222
100	1		_aTröltzsch, Fredi, _d1951-
240	1	0	_aOptimale Steuerung partieller Differentialgleichungen. _lEnglish
245	1	0	_aOptimal control of partial differential equations : _btheory, methods, and applications / _cFredi Tröltzsch ; translated by Jürgen Sprekels
264		1	_aProvidence, R.I. : _bAmerican Mathematical Society, _c[2010]
264		4	_c©2010
300			_axv, 399 pages : _billustrations ; _c26 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aGraduate studies in mathematics ; _vv. 112
504			_aIncludes bibliographical references and index
505	0	0	_t-- Introduction and examples _t-- Linear-quadratic elliptic control problems _t-- Linear-quadratic parabolic control problems _t-- Optimal control of semilinear elliptic equations _t-- Optimal control of semilinear parabolic equations _t-- Optimization problems in Banach spaces _t-- Supplementary results on partial differential equations
520			_a"Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization."--Publisher's description
650		0	_aControl theory
650		0	_aDifferential equations, Partial
650		0	_aMathematical optimization
710	2		_9111032 _aAmerican Mathematical Society.
830		0	_9110509 _aGraduate studies in mathematics, _x1065-7339 ; _vvolume 112.
900			_a31592
900			_bsatın
942			_2lcc _cKT
999			_c28455 _d28455